Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

Given a graph G, a visual cryptography scheme based on the graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper we apply maximal independent sets of the grap...

‎in this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is cohen-macaulay‎. ‎it is proved that if there exists a cover of an $r$-partite cohen-macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.

the crossing number of a graph  is the minimum number of edge crossings over all possible drawings of  in a plane. the crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and vlsi circuit design. in this paper we introduce vertex centered crossing number and study the same for maximal planar graph.

the $k$-th semi total point graph $r^k(g)$ of a graph $g$, is a graph obtained from $g$ by adding $k$ vertices corresponding to each edge and connecting them to endpoint of edge considered. in this paper, we obtain formulae for the resistance distance and kirchhoff index of $r^k(g)$.

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.

Soft set is a classification of elements the universe with respect to some given parameters. It new approach for modeling vagueness and uncertainty. The concept soft graph used provide parameterized point view graphs. In this paper we introduce concepts subdivision graph, power line investigate their properties.

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

A  $ mu $-way  $ G $-trade ($ mu geq 2) $  consists of $ mu $ disjoint decompositions of some simple (underlying) graph $ H $ into copies of a graph $ G. $  The   number of copies of the  graph $ G $ in  each of the decompositions is the volume of the $ G $-trade and   denoted by $ s. $ In this paper, we determine all values  $ s $ for which there exists a $  mu $-way   $ K_{1,m} $-trade of  vo...