منابع مشابه
On the p-domination number of cactus graphs
Let p be a positive integer and G = (V;E) a graph. A subset S of V is a p-dominating set if every vertex of V S is dominated at least p times. The minimum cardinality of a p-dominating set a of G is the p-domination number p(G): It is proved for a cactus graph G that p(G) 6 (jV j+ jLp(G)j+c(G))=2; for every positive integer p > 2; where Lp(G) is the set of vertices of G of degree at most p 1 an...
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A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...
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The problem of monitoring an electric power system is placing as few measurement devices as possible. In graph theoretical representation, it can be considered as a variant of domination problem, namely, power domination problem. This problem is to find a minimum power domination set S of a graph G = (V,E) with S ⊆ V and S can dominate all vertices and edges through the observation rules accord...
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The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2019
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2088