Various Labelling for Double Star Graph

Graph reachability is fundamental to a wide range of applications, including XML indexing, geographic navigation, Internet routing, ontology queries based on RDF/OWL, etc. Many applications involve huge graphs and require fast answering of reachability queries. Several reachability labeling methods have been proposed for this purpose. They assign labels to the vertices, such that the reachability between any two vertices may be decided using their labels only. For sparse graphs, 2-hop based reachability labeling schemes answer reachability queries efficiently using relatively small label space. However, the labeling process itself is often too time consuming to be practical for large graphs. In this paper, we propose a novel labeling scheme for sparse graphs. Our scheme ensures that graph reachability queries can be answered in constant time. Furthermore, for sparse graphs, the complexity of the labeling process is almost linear, which makes our algorithm applicable to massive datasets. Analytical and experimental results show that our approach is much more efficient than stateof- the-art approaches. Furthermore, our labeling method also provides an alternative scheme to tradeoff query time for label space, which further benefits applications that use tree-like graphs.

The paper analyses the different systems of corpus labeling, such as TODI, TOBI, and IVIE, which are three kinds of speech labeling system, and the paper puts forward a suitable labeling system of multi-modal corpus for teaching Chinese as a foreign language. The corpus includes eight levels of character description and labeling of speech tagging system. The system of labeling is applied to the improvement of the labeling method of TIMIT, which has the layer of phonetic transcription, the layer of phoneme layer, the layer of intermittent index, the lay of stress, the layer of target, the layer of phonology, and the layer of the behavior (includes the layer of posture and the layer of movement, and the layer of miscellanea. Finally, we label on the experimental corpus, and it can obtain better results in the process of teaching Chinese phonetic than before.KeywordsCorpusLabelingTeachingChinese as a foreign language

Let MAJ_n denote the Boolean majority function of n input variables. In this paper, we study the construction of depth two circuits computing MAJ_n where each gate in a circuit computes MAJ_m for m < n. We first give an explicit construction of depth two MAJ_{floor[n/2]+2} o MAJ_{ = 7 such that n congruent 3 (mod 4) where MAJ_m and MAJ_{<= m} denote the majority gates that take m and at most m distinct inputs, respectively. A graph theoretic argument developed by Kulikov and Podolskii (STACS '17, Article No. 49) shows that there is no MAJ_{<= n-2} o MAJ_{n-2} circuit computing MAJ_n. Hence, our construction reveals that the use of a smaller fan-in gates at the bottom level is essential for the existence of such a circuit. Some computational results are also provided. We then show that the construction of depth two MAJ_m o MAJ_m circuits computing MAJ_n for m<n can be translated into the construction of a newly introduced version of bipartite expander graphs which we call a list expander. Intuitively, a list expander is a c-leftregular bipartite graph such that for a given d < c, every d-leftregular subgraph of the original graph has a certain expansion property. We formalize this connection and verify that, with high probability, a random bipartite graph is a list expander of certain parameters. However, the parameters obtained are not sufficient to give us a MAJ_{n-c} o MAJ_{n-c} circuit computing MAJ_n for a large constant c.

The Combinatorial Nullstellensatz can be used to solve certain problems in combinatorics. However, one of the major complications in using the Combinatorial Nullstellensatz is ensuring that there exists a nonzero monomial. This dissertation looks at applying the Combinatorial Nullstellensatz to finding perfect matchings in bipartite graphs. The first two chapters provide background material covering topics such as linear algebra, group theory, graph theory and even the discrete Fourier transform. New results start in the third chapter, showing that the Combinatorial Nullstellensatz can be used to solve the problem of finding perfect matchings in bipartite graphs. Using the Combinatorial Nullstellensatz also allows for a vice use of matroid intersection to find the nonzero monomial. By also applying the uncertainty principle, the number of perfect matchings in a bipartite graph can be bound. The fourth chapter examines properties of the polynomials created in the use of the Combinatorial Nullstellensatz to find perfect matchings in bipartite graphs. Many of the properties of the polynomials have analogous properties for the transforms of the polynomials, which are also examined. These properties often relate back to the structure of the graph which gave rise to the polynomial. The fifth chapter provides an application of the results. Since finding a nonzero monomial can be difficult and the polynomials created in this dissertation give polynomials with such a nonzero monomial the application shows how certain polynomials can be rewritten in terms of the matching polynomials. Such a rewriting may permit an easy method to find a nonzero monomial so that the Combinatorial Nullstellensatz can be applied to the polynomial. Finally, the fifth chapter concludes with some open problems that may be areas of further research.

The development and function of tissues, blood, and the immune system is dependent upon proximity for cellular recognition and communication. However, the detection of cell-to-cell contacts is limited due to a lack of reversible, quantitative probes that can function at these dynamic sites of irregular geometry. Described here is a novel chemo-genetic tool developed for fluorescent detection of protein-protein proximity and cell apposition that utilizes the Fluorogen Activating Protein (FAP) in combination with a Dye Activated by Proximal Anchoring (DAPA). The FAP-DAPA system has two protein components, the HaloTag and FAP, expressed on separate protein targets or in separate cells. The proteins function to bind and activate a compound that has the hexyl chloride (HexCl) ligand connected to malachite green (MG), the FAP fluorogen, via a poly(ethylene glycol) spacer spanning up to 28 nm. The dehalogenase protein, HaloTag, covalently binds the HexCl ligand, locally concentrating the attached MG. If the FAP is within range of the anchored fluorogen, it will bind and activate MG specifically when the bath concentration is too low to saturate the FAP receptor. A new FAP variant was isolated with a 1000-fold reduced KD of ∼10-100 nM so that the fluorogen activation reports proximity without artificially enhancing it. The system was characterized using purified FRB and FKBP fusion proteins and showed a doubling of fluorescence upon rapamycin induced complex formation. In cocultured HEK293 cells (HaloTag and FAP-expressing) fluorescence increased at contact sites across a broad range of labeling conditions, more reliably providing contact-specific fluorescence activation with the lower-affinity FAP variant. When combined with suitable targeting and expression constructs, this labeling system may offer significant improvements in on-demand detection of intercellular contacts, potentially applicable in neurological and immunological synapse measurements and other transient, dynamic biological appositions that can be perturbed using other labeling methods that stabilize these interactions.

Characterizing bipartite Toeplitz graphs

Let be a graph with p vertices and q edges. We have introduced a new graph labeling method using integers and cordial-related works and investigated some graphs for this labeling technique. Using this labeling concept, we have examined the graphs like path, cycle, star, complete graph, comb, and wheel graph. The first research paper on graph theory was published by Leonhard Euler. However, he did not use the word ‘graph’ in his work. In the early stages of the development of the subject, the vertices of a graph were specified as , and the edges were denoted by, . In recent times, several researchers have attempted to provide different types of labeling to the vertices and edges of a graph by identifying the relevant mathematical properties. The present paper provides a novel method of labeling by employing integers, which may form a foundation for future research work. In this paper, we investigate the pair mean cordial labeling behavior of some cycle-related graphs like the ice cream graph, closed web graph, circulant graph, zig-zag chord graph, pentagonal circular ladder, djembe graph, quadrilateral friendship graph, and origami graph.

Axiomatic characterization of the interval function of a bipartite graph

Let k be a positive integer. Let G be a graph of order $$n\ge 3$$n?3 and W a subset of V(G) with $$|W|\ge 3k$$|W|?3k. Wang (J Graph Theory 78:295---304, 2015) proved that if $$d(x)\ge 2n/3$$d(x)?2n/3 for each $$x\in W$$x?W, then G contains k vertex-disjoint cycles such that each of them contains at least three vertices of W. In this paper, we obtain an analogue result of Wang's Theorem in bipartite graph with the partial degree condition. Let $$G=(V_1,V_2;E)$$G=(V1,V2?E) be a bipartite graph with $$|V_1|=|V_2|=n$$|V1|=|V2|=n, and let W be a subset of $$V_1$$V1 with $$|W|\ge 2k$$|W|?2k, where k is a positive integer. We show that if $$d(x)+d(y)\ge n+k$$d(x)+d(y)?n+k for every pair of nonadjacent vertices $$x\in W, y\in V_2$$x?W,y?V2, then G contains k vertex-disjoint cycles such that each of them contains at least two vertices of W.

The Implementation Of Bipartite Graph To Minimize Crossing Number Problem Of Crossroads In Manado. Supervised by BENNY PINONTAN as main supervisor and CHRIESTIE E. J. C. MONTOLALU as co-supervisor. In general, the crossroads are the meeting points of two-way roads from four different places. This causes cross direction at that point. There are various methods that can be used to minimize the crossing number problem crossroad, for example graph theory. The ability of graph theory can later help describe crossroads in Manado into graph, with nodes and lines. In this case, the crossing number problems will solve by bipartite graph. Bipartite graph is a graph that does not have an odd cycle, and can be partitioned into two parts of a set of vertices. Based on results of this research, the appropriate form of the bipartite graph is and in two different form. First, with an isolated vertex, and second, without isolated vertex. In the case of crossroads, Bipartite graph turns out to be one method that is very suitable and helps determine the crossing number and its solution quickly.

We develop a bipartite rigidity theory for bipartite graphs parallel to the classical rigidity theory for general graphs, and define for two positive integers k , l k,l the notions of ( k , l ) (k,l) -rigid and ( k , l ) (k,l) -stress free bipartite graphs. This theory coincides with the study of Babson–Novik’s balanced shifting restricted to graphs. We establish bipartite analogs of the cone, contraction, deletion, and gluing lemmas, and apply these results to derive a bipartite analog of the rigidity criterion for planar graphs. Our result asserts that for a planar bipartite graph G G its balanced shifting, G b G^b , does not contain K 3 , 3 K_{3,3} ; equivalently, planar bipartite graphs are generically ( 2 , 2 ) (2,2) -stress free. We also discuss potential applications of this theory to Jockusch’s cubical lower bound conjecture and to upper bound conjectures for embedded simplicial complexes.

One of the topics in graph theory that is interesting and developed continuously is metric dimension. It has some new variation concepts, such as star metric dimension. The order set of Z={z1,z2,…,zn }⊆V(G) called star resolving set of connected graph G if Z is Star Graph and for every vertex in G has different representation to the set Z. The representation is expressed as the distance d(u,z), it is the shortest path from vertex u to z for every u,z∈V(G). Star basis of a graph is the smallest cardinality of star resolving set. The number of vertex in star basis is called star metric dimension of G which denoted by Sdim(G). The purpose of this article is to determine the characteristic of star metric dimension and the value of star metric dimension of some classes of graphs. The method which is used in this study is library research. Some of the results of this research are complete graph has Sdim(Kn )=n-1, for n≥3, bipartite graph K(2,n) has Sdim (K(2,n) )=n, for n≥3. Besides complete bipartite graph hasn’t star metric dimension or for m,n≥3 or it can said that Sdim (K(m,n) )=0. Another graph, that is Fan graph has Sdim (Fn )=2 for 2≤n≤5 and for n≥6 Sdim (Fn )=(2n+3)/5.

Following this advice, we should look over the big questions, then doodle and sketch out some approaches. If you are an expert, then this is easy to do, but most people do not want to wait to become an expert before looking at interesting problems. Graph theory, our area of expertise, has many hard-to-solve questions. Some hark back to the recreational roots of the area yet still keep their mystery. These ‘‘acorns’’ can be planted on the backs of envelopes, on a blackboard, and over a coffee. Our goal is to collect some of these conjectures—arguably some of the most intriguing—in one place. We present ten conjectures in graph theory, and you can read about each one in at most ten minutes. As we live in the era of Twitter, all the conjectures we state are 140 characters or fewer (so ‘‘minute’’ here has a double meaning). We might even call these sketchy tweets, as we present examples for each conjecture that you can doodle on as you read. Hamming also references ambiguity: good researchers can work both on proving and disproving the same statement, so we approach the conjectures with an open mind. He also mentions that a good approach is to reframe the problem, and change the point of view. One example from Vizing’s Conjecture (which is discussed as our second-to-last conjecture in the following text), is the three-page paper [2] which, with a new way of thinking, reduced most of the published work of twenty years to a corollary of its main result! Given the size of modern graph theory, with its many smaller subfields (such as structural graph theory, random graphs, topological graph theory, graph algorithms, spectral graph theory, graph minors, and graph homomorphisms, to name a few), it would be impossible to list all, or even the bulk of the conjectures in the field. We are content instead to focus on a few family jewels, which have an intrinsic beauty and have provided some challenges for graph-theorists for at least two decades. There is something for everyone here, from undergraduate students taking their first course in graph theory, to seasoned researchers in the field. For additional reading on problems and conjectures in graph theory and other fields, see the Open Problem Garden maintained by IRMACS at Simon Fraser University [24]. We consider only finite and undirected graphs, with no multiple edges or loops (unless otherwise stated). We assume the reader has some basic familiarity with graphs and their terminology, including notions such as cycles, paths, complete graphs, complete bipartite graphs, vertex degrees, and connected graphs. We use the notation Cn for the cycle with n vertices, Pn for the path with n vertices, and Kn for the complete graph with n vertices. The complete bipartite graph with m and n vertices of the respective colors is denoted by Km,n. All the background we need can be found in any text in graph theory, such as those of Diestel [9] and West [41], or online (see for example [42]).

This article proposes an empirical study of the LCD controller circuit. We model a component-netlable double-mode network using bipartite graph, and two different networks named components network and netlables network are created based on the bipartite graph model. We calculates degree distribution, edges weight distribution, nodes weight distribution for bipartite graph and average path distance, clustering coefficients, degree distribution, edges weight distribution, nodes weight distribution for single-mode networks respectively. Some analyses have been made according to the topological statistical parameters. Theory of bipartite graph used in integrated circuit offers a new perspective for us to analyze integrated circuit system.

Electron microscopy (EM) is one of the most efficient methods for studying the fine structure of cells with a resolution thousands of times higher than that of visible light microscopy. The most advanced implementation of electron microscopy in biology is EM tomography of samples stabilized by freezing without water crystallization (cryoET). By circumventing the drawbacks of chemical fixation and dehydration, this technique allows investigating cellular structures in three dimensions at the molecular level, down to resolving individual proteins and their subdomains. However, the problem of efficient identification and localization of objects of interest has not yet been solved, thus limiting the range of targets to easily recognizable or abundant subcellular components. Labeling techniques provide the only way for locating the subject of investigation in microscopic images. CryoET imposes conflicting demands on the labeling system, including the need to introduce into a living cell the particles composed of substances foreign to the cellular chemistry that have to bind to the molecule of interest without disrupting its vital functions and physiology of the cell. Thisreview examines both established and prospective methods for selective labeling of proteins and subcellular structures aimed to enable their localization in cryoET images.