‎the annihilator graph $ag(r)$ of a commutative ring $r$ is a simple undirected graph with the vertex set $z(r)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$‎. ‎in this paper we give the sufficient condition for a graph $ag(r)$ to be complete‎. ‎we characterize rings for which $ag(r)$ is a regular graph‎, ‎we show that $gamma (ag(r))in {1,2}$ and...

Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i  v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih  v  v  v  over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

let g be a simple connected graph and {v1, v2, …, vk} be the set of pendent (vertices ofdegree one) vertices of g. the reduced distance matrix of g is a square matrix whose (i,j)–entry is the topological distance between vi and vj of g. in this paper, we obtain the spectrumof the reduced distance matrix of thorn graph of g, a graph which obtained by attaching somenew vertices to pendent vertice...

‎the narumi-katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎let $g$ be a ‎simple graph with vertex set $v = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $g$‎. ‎the narumi-katayama ‎index is defined as $nk(g) = prod_{vin v}d(v)$‎. ‎in this paper,‎ ‎the narumi-katayama index is generalized using a $n$-ve...

Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most  colours, which is for a fixed graph G , a polynomial in  , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.

The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.

Let G be a simple graph with vertex set V (G). The common neighborhood graph or congraph of G, denoted by con(G), is a graph with vertex set V (G), in which two vertices are adjacent if and only if they have at least one common neighbor in G. We compute the congraphs of some composite graphs. Using these results, the congraphs of several special graphs are determined.

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

let $g$ be a finite group and $gamma(g)$ the prime graph of $g$‎. ‎recently people have been using prime graphs to study simple groups‎. ‎naturally we pose a question‎: ‎can we use prime graphs to study almost‎ ‎simple groups or non-simple groups? in this paper some results in‎ ‎this respect are obtained and as follows‎: ‎$gcong s_p$ if and only‎ ‎if $|g|=|s_p|$ and $gamma(g)=gamma(s_p)$‎, ‎whe...