Perfect secure domination in graphs

Perfect secure domination in graphs

Blog Article

Let $G=(V,E)$ be a graph.A subset $S$ of $V$ is a dominating set ilootpaperie 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 $v$ 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 sequal eclipse 5 battery of a perfect secure dominating set 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.