Perfect secure domination in graphs

Perfect secure domination in graphs

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Let $G=(V,E)$ be a graph.A subset $S$ of $V$ is a dominating set of $G$ if every vertex in $Vsetminus S$ is adjacent to a vertex in $S.$ A dominating set $S$ is called a secure dominating set if for each $vin Vsetminus S$ there exists $uin S$ such that ps5 price new jersey $v$ is adjacent to $u$ and $S_1=(Ssetminus{u})cup {v}$ is a dominating set.If further the vertex $uin S$ is unique, then $S$ is called a perfect secure dominating set.The minimum cardinality of a perfect secure dominating set wac 4011 of $G$ is called the perfect secure domination number of $G$ and is denoted by $gamma_{ps}(G).

$ In this paper we initiate a study of this parameter and present several basic results.