‎in this paper we defined the vertex removable cycle in respect of the following‎, ‎if $f$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$g in f $‎, ‎the cycle $c$ in $g$ is called vertex removable if $g-v(c)in in f $.‎ ‎the vertex removable cycles of eulerian graphs are studied‎. ‎we also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎

in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

‎in this paper we introduce the concept of order difference interval graph $gamma_{odi}(g)$ of a group $g$‎. ‎it is a graph $gamma_{odi}(g)$ with $v(gamma_{odi}(g)) = g$ and two vertices $a$ and $b$ are adjacent in $gamma_{odi}(g)$ if and only if $o(b)-o(a) in [o(a)‎, ‎o(b)]$‎. ‎without loss of generality‎, ‎we assume that $o(a) leq o(b)$‎. ‎in this paper we obtain several properties of $gamma_...

‎In this paper we defined the vertex removable cycle in respect of the following‎, ‎if $F$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$G in F $‎, ‎the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $.‎ ‎The vertex removable cycles of eulerian graphs are studied‎. ‎We also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎    

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 a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...

recently, e. m'{a}v{c}ajov'{a} and m. v{s}koviera proved that every bidirected eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. this result shows the validity of bouchet's nowhere zero conjecture for eulerian bidirected graphs. in this paper we prove the same theorem in a different terminology and with a short and simple proof. more precisely, we p...