Vertex Domination Critical in Circulant Graphs
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چکیده
منابع مشابه
Domination in Circulant Graphs
A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G− v is less than the total domination number of G. We call these graphs γt-critical. In this paper, we determine the domination and the total domination number in the Circulant graphs Cn〈1, 3〉, and then study γ-criticality...
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The bondage number of a graph G is the minimum number of edges whose removal results in a graph with larger domination number.A dominating setD is called an efficient dominating set ofG if |N−[v]∩D|=1 for every vertex v ∈ V (G). In this paper we establish a tight lower bound for the bondage number of a vertex-transitive graph. We also obtain upper bounds for regular graphs by investigating the ...
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Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:Vrightarrow{0,1,2,3}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DR...
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For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by removing a single vertex from $G$ has at least one EDS, and (ii) a hypo-unique domination graph (a hypo-$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets...
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تاریخ انتشار 2017