Maryam Atapour
Department of Mathematics Faculty of basic sciences University of Bonab Bonab, Iran, Po. Box: 5551761167
[ 1 ] - Twin minus domination in directed graphs
Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...
[ 2 ] - Eternal m-security subdivision numbers in graphs
An eternal $m$-secure set of a graph $G = (V,E)$ is aset $S_0subseteq V$ that can defend against any sequence ofsingle-vertex attacks by means of multiple-guard shifts along theedges of $G$. A suitable placement of the guards is called aneternal $m$-secure set. The eternal $m$-security number$sigma_m(G)$ is the minimum cardinality among all eternal$m$-secure sets in $G$. An edge $uvin E(G)$ is ...
[ 3 ] - Eternal m- Security Subdivision Numbers in Graphs
Let be a simple graph with vertex set and edges set . A set is a dominating set if every vertex in is adjacent to at least one vertex in . An eternal 1-secure set of a graph G is defined as a dominating set such that for any positive integer k and any sequence of vertices, there exists a sequence of guards with and either or and is a dominating set. If we take a guard on every ver...
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