The paper deals with a digraph non-negative vertex weights. A subset \(W\) of the set vertices is called dominating if any that not belongs to it reachable from within precisely one step. minimal ceases be when removing it. investigates problem searching for maximum weight in vertex-weighted digraph. An integer linear programming model proposed this problem. tested on random instances and real ...

let g be a fixed element of a finite group g. we introduce the g-noncommuting graph of g whose vertex set is whole elements of the group g and two vertices x,y are adjacent whenever [x,y] g  and  [y,x] g. we denote this graph by . in this paper, we present some graph theoretical properties of g-noncommuting graph. specially, we investigate about its planarity and regularity, its clique number a...

In a signed graph G, a negative clique is a complete subgraph having negative edges only. In this article, we give characteristic polynomial expressions, and eigenvalues of some signed graphs having negative cliques. This includes signed cycle graph, signed path graph, a complete graph with disjoint negative cliques, and star block graph with negative cliques.

We prove that every cubic bridgeless graph G contains a 2-factor which intersects all (minimal) edge-cuts of size 3 or 4. This generalizes an earlier result of the authors, namely that such a 2-factor exists provided that G is planar. As a further extension, we show that every graph contains a cycle (a union of edge-disjoint circuits) that intersects all edge-cuts of size 3 or 4. Motivated by t...

A edge 2-rainbow dominating function (E2RDF) of a graph G is a ‎function f from the edge set E(G) to the set of all subsets‎ ‎of the set {1,2} such that for any edge.......................

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

A Graph G is Super Strongly Perfect Graph if every induced sub graph H of G possesses a minimal dominating set that meets all the maximal complete sub graphs of H. In this paper we have analyzed the structure of super strongly perfect graphs in some Interconnection Networks, like Mesh, Torus, Hyper cubes and Grid Networks. Along with this investigation, we have characterized the Super Strongly ...

We prove that every cubic bridgeless graph G contains a 2-factor which intersects all (minimal) edge-cuts of size 3 or 4. This generalizes an earlier result of the authors, namely that such a 2-factor exists provided that G is planar. As a further extension, we show that every graph contains a cycle (a union of edge-disjoint circuits) that intersects all edge-cuts of size 3 or 4. Motivated by t...

Given a graph $G=(V,E)$ and a vertex $v in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:Vrightarrow {0,1,2}$ be a function on $G$. The weight of $f$ is $omega(f)=sum_{vin V}f(v)$ and let $V_i={vin V colon f(v)=i}$, for $i=0,1,2$. The function $f$ is said to bebegin{itemize}item a Roman ${2}$-dominating function, if for every vertex $vin V_0$, $sum_{uin N(v)}f(u)geq 2$. The R...