the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

a 1993 result of j. llibre, and m. misiurewicz, (theorem a [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. also a 1980 result of l.s. block, j. guckenheimer, m. misiurewicz and l.s. young (lemma 1.5 [3]) states that if g is an a-graph of f then h(g) ? h( f ). in this pap...

let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

 Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...

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.

the neighbourhood polynomial g , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. in other word $n(g,x)=sum_{uin n(g)} x^{|u|}$, where n(g) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. in this paper we compute this polynomial for some na...

Let $P(G,lambda)$ be the chromatic polynomial of a graph $G$. A graph $G$ ischromatically unique if for any graph $H$, $P(H, lambda) = P(G,lambda)$ implies $H$ is isomorphic to $G$. In this paper, we determine the chromaticity of all Tur'{a}n graphs with at most three edges deleted. As a by product, we found many families of chromatically unique graphs and chromatic equivalence classes of graph...

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 $g_1$, $g_2$, ..., $...