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...

let $g$ be a connected graph, and let $d[g]$ denote the double graph of $g$. in this paper, we first derive closed-form formulas for different distance based topological indices for $d[g]$ in terms of that of $g$. finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topologica...

the non commuting graph of a non-abelian finite group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we prove some new results about this graph. in particular we will give a new proof of theorem 3.24 of [2]. we also prove that if $g_1$, $g_2$, ..., $...

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

Let $G$ be a graph with $p$ vertices and $q$ edges. The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)cup E(G)$ to ${0, pm 1, pm2, dots, pm (frac{p+q-1}{2})}$ when $p+q$ is odd and from $V(G)cup E(G)$ to ${pm 1, pm 2, dots, pm (frac{p+q}{2})}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a {...