Garrett College Research Papers & Analytics Data

Research Article
10.5281/zenodo.8072171

New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Reverse Dimension Dominating As Hyper Dimple On Super Dimity

Jun 22, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

Research Article
10.5281/zenodo.8062016

New Ideas On Super Dimity By Hyper Dimple Of Dimension Dominating In Recognition of Cancer With (Neutrosophic) SuperHyperGraph

Jun 20, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

Research Article
10.5281/zenodo.8052925

New Ideas On Super Con By Hyper Conceit Of Connective Dominating In Recognition of Cancer With (Neutrosophic) SuperHyperGraph

Jun 18, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

Supplementary Content
10.5281/zenodo.8027488

United Dominating In SuperHyperGraphs

Jun 12, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

Supplementary Content
10.5281/zenodo.8020181

Zero Forcing In SuperHyperGraphs

Jun 09, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

“Book #175” [ADDRESSED CITATION] [HG175b] Henry Garrett, “Zero Forcing In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.8020181). @googlebooks:https://books.google.com/books/about?id=- @GooglePlay:https://play.google.com/store/books/details?id=- @ResearchGate: https://www.researchgate.net/publication/- @WordPress: https://drhenrygarrett.wordpress.com/2023/07/22/Zero-Forcing-In-SuperHyperGraphs/ @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/8020181 @academia:https://www.academia.edu/- Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle   [ADDRESSED CITATION] [HG175b] Henry Garrett, “Zero Forcing In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.8020181). In this scientific research book, there are some scientific research chapters on “Extreme Zero Forcing In SuperHyperGraphs” and “Neutrosophic Zero Forcing In SuperHyperGraphs” about some scientific researches on Zero Forcing In SuperHyperGraphs by two (Extreme/Neutrosophic) notions, namely, Extreme Zero Forcing In SuperHyperGraphs and Neutrosophic Zero Forcing In SuperHyperGraphs. With scientific research on the basic scientific research properties, the scientific research book starts to make Extreme Zero Forcing In SuperHyperGraphs theory and Neutrosophic Zero Forcing In SuperHyperGraphs theory more (Extremely/Neutrosophicly) understandable. Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4048 readers in Scribd. It’s titled “Beyond Neutrosophic Graphs” and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. [Ref] Henry Garrett, (2022). “Beyond Neutrosophic Graphs”, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 5046 readers in Scribd. It’s titled “Neutrosophic Duality” and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and Zero Forcing In SuperHyperGraphs in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It’s smart to consider a set but acting on its complement that what’s done in this research book which is popular in the terms of high readers in Scribd. [Ref] Henry Garrett, (2022). “Neutrosophic Duality”, Florida: GLOBAL KNOW- LEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf).   There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them. \\ The seminal paper and groundbreaking article is titled ``\textit{New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph As Hyper Tool On Super Toot}'' in \textbf{Ref.} \cite{HG11s} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms with introducing used neutrosophic classes of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “\textit{Current Trends in Mass Communication (CTMC)}” with ISO abbreviation ``\textit{J Curr Trends Comp Sci Res}'' in volume 1 and issue 1 with pages 37-60. \\ The seminal paper and groundbreaking article is titled ``\textit{Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer’s Treatments}'' in \textbf{Ref.} \cite{HG22s} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer’s Treatments. It's published in prestigious and fancy journal is entitled “\textit{Journal of Mathematical Techniques and Computational Mathematics(JMTCM)}” with ISO abbreviation ``\textit{J Math Techniques Comput Math}'' in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It's the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``\textit{A Research on Cancer's Recognition and Neutrosophic Super Hypergraph by Eulerian Super Hyper Cycles and Hamiltonian Sets as Hyper Covering Versus Super separations}'' in \textbf{Ref.} \cite{HG33s} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer’s Recognition. It's published in prestigious and fancy journal is entitled “\textit{Journal of Mathematical Techniques and Computational Mathematics(JMTCM)}” with ISO abbreviation ``\textit{J Math Techniques Comput Math}'' in volume 2 and issue 3 with pages 136-148. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It's the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``\textit{Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes}'' in \textbf{Ref.} \cite{HG44s} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “\textit{Journal of Mathematical Techniques and Computational Mathematics(JMTCM)}” with ISO abbreviation ``\textit{J Math Techniques Comput Math}'' in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It's the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. The seminal paper and groundbreaking article is titled ``\textit{neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs}'' in \textbf{Ref.} \cite{HG55s} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “\textit{Journal of Current Trends in Computer Science Research (JCTCSR)}” with ISO abbreviation ``\textit{J Curr Trends Comp Sci Res}'' in volume 2 and issue 1 with pages 16-24. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It's the breakthrough toward independent results based on initial background. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It's the breakthrough toward independent results based on initial background. In some articles are titled ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph}'' in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),  ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs}'' in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),  ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer’s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}'' in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer’s Recognition}'' in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer’s Recognition On Neutrosophic SuperHyperGraphs}'' in \textbf{Ref.} \cite{HG8} by Henry Ga

Research Article
10.5281/zenodo.7857841

New Ideas On Super Nebulous By Hyper Nebbish Of Eulerian-Cycle-Neighbor In Recognition of Cancer With (Neutrosophic) SuperHyperGraph

Apr 24, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

256 Henry Garrett, “New Ideas On Super Nebulous By Hyper Nebbish Of Eulerian-Cycle-Neighbor In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7857841). @ResearchGate: https://www.researchgate.net/publication/- @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/7857841 @academia: https://www.academia.edu/- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Nebulous By Hyper Nebbish Of Eulerian-Cycle-Neighbor In Recognition of Cancer With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyper{\tiny Eulerian-Cycle-Neighbor}). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a {\tiny Eulerian-Cycle-Neighbor} pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V'=\{V_1,V_2,\ldots,V_s\}$ and $E'=\{E_1,E_2,\ldots,E_z\}.$ Then either $V'$ or $E'$ is called Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor} if the following expression is called Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor} criteria holds \begin{eqnarray*} && \forall N(E_a)\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the all number of SuperHyperEdges}; \end{eqnarray*} Neutrosophic re-SuperHyper{\tiny Eulerian-Cycle-Neighbor} if the following expression is called Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor} criteria holds \begin{eqnarray*} && \forall N(E_a)\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the all number of SuperHyperEdges}; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor} if the following expression is called Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor} criteria holds \begin{eqnarray*} && \forall N(V_a)\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the all number of SuperHyperEdges}; \end{eqnarray*} Neutrosophic rv-SuperHyper{\tiny Eulerian-Cycle-Neighbor} if the following expression is called Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor} criteria holds \begin{eqnarray*} && \forall N(V_a)\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the all number of SuperHyperEdges}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyper{\tiny Eulerian-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Cycle-Neighbor}. ((Neutrosophic) SuperHyper{\tiny Eulerian-Cycle-Neighbor}). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyper{\tiny Eulerian-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Cycle-Neighbor} and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the conseNeighborive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Eulerian-Cycle-Neighbor}; a Neutrosophic SuperHyper{\tiny Eulerian-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Cycle-Neighbor} and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Eulerian-Cycle-Neighbor}; an Extreme SuperHyper{\tiny Eulerian-Cycle-Neighbor} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Cycle-Neighbor} and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality conseNeighborive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Eulerian-Cycle-Neighbor}; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyper{\tiny Eulerian-Cycle-Neighbor} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Cycle-Neighbor} and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Eulerian-Cycle-Neighbor}; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyper{\tiny Eulerian-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Cycle-Neighbor}, Neutrosophi

Supplementary Content
10.5281/zenodo.7857906

Eulerian-Cycle-Neighbor In SuperHyperGraphs

Apr 24, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

Supplementary Content
10.5281/zenodo.7848019

Eulerian-Type-Path-Decomposition In SuperHyperGraphs

Apr 20, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

“Book #163” [ADDRESSED CITATION] [HG163b] Henry Garrett, “Eulerian-Type-Path-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7848019). @googlebooks:https://books.google.com/books/about?id=- @GooglePlay:https://play.google.com/store/books/details?id=- @ResearchGate: https://www.researchgate.net/publication/- @WordPress: https://drhenrygarrett.wordpress.com/2023/07/22/Eulerian-Type-Path-Decomposition-In-SuperHyperGraphs/ @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/7848019 @academia:https://www.academia.edu/- Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle — — “Book #163” [ADDRESSED CITATION] [HG163b] Henry Garrett, “Eulerian-Type-Path-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7848019). #Link (KE): https://www.amazon.com/dp/- (SC): https://www.amazon.com/dp/- (HC): https://www.amazon.com/dp/- #ISBN CC BY-NC-ND 4.0 - &lrm;- — Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle —   [ADDRESSED CITATION] [HG163b] Henry Garrett, “Eulerian-Type-Path-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7848019). In this scientific research book, there are some scientific research chapters on “Extreme Eulerian-Type-Path-Cut In SuperHyperGraphs ” and “Neutrosophic Eulerian-Type-Path-Cut In SuperHyperGraphs ” about some scientific researches on Eulerian-Type-Path-Cut In SuperHyperGraphs by two (Extreme/Neutrosophic) notions, namely, Extreme Eulerian-Type-Path-Cut In SuperHyperGraphs and Neutrosophic Eulerian-Type-Path-Cut In SuperHyperGraphs . With scientific researches on the basic properties, the scientific research book starts to make Extreme Eulerian-Type-Path-Cut In SuperHyperGraphs theory and Neutrosophic Eulerian-Type-Path-Cut In SuperHyperGraphs theory more (Extremely/Neutrosophicly) understandable. Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It’s titled “Beyond Neutrosophic Graphs” and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. [Ref] Henry Garrett, (2022). “Beyond Neutrosophic Graphs”, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It’s titled “Neutrosophic Duality” and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and Eulerian-Type-Path-Cut In SuperHyperGraphs in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It’s smart to consider a set but acting on its complement that what’s done in this research book which is popular in the terms of high readers in Scribd. [Ref] Henry Garrett, (2022). “Neutrosophic Duality”, Florida: GLOBAL KNOW- LEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). — 248 Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Eulerian-Type-Path-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7840206). @ResearchGate: https://www.researchgate.net/publication/370074278 @Scribd: https://www.scribd.com/document/639129547 @ZENODO_ORG: https://zenodo.org/record/7840206 @academia: https://www.academia.edu/100379583 — 249 Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Type-Path-Decomposition As Hyper Decompress On Super Decompensation”, Zenodo 2023, (doi: 10.5281/zenodo.7839333). @ResearchGate: https://www.researchgate.net/publication/370070007 @Scribd: https://www.scribd.com/document/639059148 @ZENODO_ORG: https://zenodo.org/record/7839333 @academia: https://www.academia.edu/100359428 — — “Book #163” [ADDRESSED CITATION] [HG163b] Henry Garrett, “Eulerian-Type-Path-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7848019). @googlebooks:https://books.google.com/books/about?id=- @GooglePlay:https://play.google.com/store/books/details?id=- @ResearchGate: https://www.researchgate.net/publication/- @WordPress: https://drhenrygarrett.wordpress.com/2023/07/22/Eulerian-Type-Path-Decomposition-In-SuperHyperGraphs/ @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/7848019 @academia:https://www.academia.edu/- Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle — — “Book #163” [ADDRESSED CITATION] [HG163b] Henry Garrett, “Eulerian-Type-Path-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7848019). #Link (KE): https://www.amazon.com/dp/- (SC): https://www.amazon.com/dp/- (HC): https://www.amazon.com/dp/- #ISBN CC BY-NC-ND 4.0 - - — Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle — -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle —

Research Article
10.5281/zenodo.7839333

New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Type-Path-Decomposition As Hyper Decompress On Super Decompensation

Apr 18, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Eulerian-Type-Path-Decomposition As Hyper Decompress On Super Decompensation } } \newline \newline Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyper{\tiny Eulerian-Type-Path-Decomposition}). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a {\tiny Eulerian-Type-Path-Decomposition} pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V'=\{V_1,V_2,\ldots,V_s\}$ and $E'=\{E_1,E_2,\ldots,E_z\}.$ Then either $V'$ or $E'$ is called Neutrosophic e-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} if the following expression is called Neutrosophic e-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} criteria holds   \begin{eqnarray*} && \forall E'\in P: P~\text{is} \\&& \text{a SuperHyperPath and it has} \\&&  \text{the maximum number of SuperHyperEdges}; \end{eqnarray*}  Neutrosophic re-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} if the following expression is called Neutrosophic e-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} criteria holds   \begin{eqnarray*} && \forall E'\in P: P~\text{is} \\&& \text{a SuperHyperPath and it has} \\&&  \text{the maximum number of SuperHyperEdges}; \end{eqnarray*}  and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}  if the following expression is called Neutrosophic v-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} criteria holds   \begin{eqnarray*} && \forall V'\in P: P~\text{is} \\&& \text{a SuperHyperPath and it has} \\&&  \text{the maximum number of SuperHyperEdges}; \end{eqnarray*}   Neutrosophic rv-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} if the following expression is called Neutrosophic v-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} criteria holds   \begin{eqnarray*} && \forall V'\in P: P~\text{is} \\&& \text{a SuperHyperPath and it has} \\&&  \text{the maximum number of SuperHyperEdges}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyper{\tiny Eulerian-Type-Path-Decomposition} if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic re-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic v-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}. ((Neutrosophic) SuperHyper{\tiny Eulerian-Type-Path-Decomposition}).  Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyper{\tiny Eulerian-Type-Path-Decomposition} if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic re-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic v-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the conseNeighborive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Eulerian-Type-Path-Decomposition}; a Neutrosophic SuperHyper{\tiny Eulerian-Type-Path-Decomposition} if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic re-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic v-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} and $\mathcal{C}(NSHG)$ for a  Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality  conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Eulerian-Type-Path-Decomposition}; an Extreme SuperHyper{\tiny Eulerian-Type-Path-Decomposition} SuperHyperPolynomial  if it's either of Neutrosophic e-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic re-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, Neutrosophic v-SuperHyper{\tiny Eulerian-Type-Path-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Eulerian-Type-Path-Decomposition} and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality conseNeighborive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the E

Supplementary Content
10.5281/zenodo.7812750

Eulerian-Path-Cut In SuperHyperGraphs

Apr 10, 2023
Zenodo (CERN European Organization for Nuclear Research)
Henry Garrett

Garrett College

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