the first geometric-arithmetic index was introduced in the chemical theory as the summationof 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertexu. in this paper we give the expressions for computing the first geometric-arithmetic index ofhexagonal systems and phenylenes and present new method for describing hexagonal systemby corresponding a simple graph...

let $g$ be a finite simple graph whose vertices and edges are weighted by two functions. in this paper we shall define and calculate entropy of a dynamical system on weights of the graph $g$, by using the weights of vertices and edges of $g$. we examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. at the end it is shown that, for $rin [0,+infty]$, t...

The prime graph of a finite group $G$ is denoted by $Gamma(G)$ whose vertex set is $pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $Gamma(H)=Gamma(G)$, in while $Hnotcong G$. In this paper, we consider finite groups with the same prime gr...

‎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 connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...