The deg-centric graph of a simple, connected graph G, denoted by Gd, is a graph constructed from G such that V(Gd) = V(G) and E(Gd) = {vivj : dG(v_i,v_j) ≤ degG(v_i)}. This paper presents the Roman domination number of deg-centric graphs. Also, investigate the properties and structural characteristics of this type of graph

Coloring and domination in graphs are two well explored areas of research in graph theory. Blending these notions, the dominator coloring of graphs was introduced in the literature; following which several variants of domination related coloring patterns have been defined and studied, based on different types of coloring and domination in graphs. A vertex coloring of a graph that demands the existence of a path in which every internal vertex between two vertices has a unique color is called a rainbow vertex coloring of the graph. In this article, we investigate the rainbow dominator coloring of graphs; a vertex coloring that combines the concepts of rainbow vertex coloring and dominator coloring of graphs. We discuss some properties of the rainbow dominator coloring of graphs and determine the rainbow dominator chromatic number of certain classes of graphs and their complements.

n this manuscript, we obtain refinements of the Hermite-Hadamard type inequalites for func- tions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically ρ-convex. We also show that our results coincide with previous results

The derived numbers of a real function at a point of its domain provide useful information about the variation of the function around that point. In this note, we introduce the concept of one-sided derived numbers and we obtain specific characterizations of some functional properties. We exemplify the usefulness of our results through some interesting consequences and applications.

Let $ G=G(V,E) $ be a graph. A set $ S\subseteq V $ is a power dominating set of $ G $ if $ S $ observes all the vertices in $ V,$ following two rules: domination and propagation. The cardinality of a minimum power dominating set is called the power domination number. In this paper, we compute the power domination number of generalized $ m $-Mycielskian of a cycle, $ C_n $. We found that it depends on the numbers $ n \an m $.

We study fusion frame in tensor product of Hilbert spaces and discuss some of its properties.\,The resolution of the identity operator on a tensor product of Hilbert spaces is being discussed.\,An alternative dual of a fusion frame in tensor product of Hilbert spaces is also presented.

n our present research, we investigate a new class of polynomials which we call the associated polynomials. Firstly, we drive a general identity which generalizes the Laguerre transform of a sequence. More precisely, we give a three-term recurrence formula for calculating the associated polynomials. Secondly, as an application, we define the associated Fibonacci polynomials.

This article is to study the notions of hesitant fuzzy minimal clopen and hesitant fuzzy maximal clopen sets. In this article, we have proved hesitant fuzzy maximal and minimal clopen sets are independent to hesitant fuzzy minimal and maximal open sets(resp. closed sets). Using hesitant fuzzy disconnectedness certain properties of both hesitant fuzzy minimal and maximal clopen sets are discussed.

A 1-fold of $G$ is the graph $G'$ obtained from a graph $G$ by identifying two nonadjacent vertices in $G$ having at least one common neighbor and reducing the resulting multiple edges to simple edges. A sequence of graphs $G = G_0, G_1, G_2, \ldots ,G_k$, where $G_{i+1}$ is a 1-fold of $G_{i}$ for $i=0,1,2,\ldots ,k-1$ is called a uniform $k$-folding if all the graphs in the sequence are singular or all of them are nonsingular. The largest $k$ for which there exists a uniform $k$- folding of $G$ is called fold thickness of $G$ and it was first introduced in [Campe{\~n}a, F. J. H.; Gervacio, S. V. On the fold thickness of graphs. \emph{Arab, J. Math. (Springer)} {\bf9} (2020), no. 2, 345--355]. In this paper, we determine fold thickness of $K_n \odot \overline{K_m}$, $K_n + \overline{K_m}$, cone graph and tadpole graph.