%0 Journal Article
%T Perfect secure domination in graphs
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Rashmi, S.V. Divya
%A Arumugam, Subramanian
%A Bhutani, Kiran R.
%A Gartland, Peter
%D 2017
%\ 07/01/2017
%V 7
%N Special Issue on the Occasion of Banaschewski's 90th Birthday (II)
%P 125-140
%! Perfect secure domination in graphs
%K Secure domination
%K perfect secure domination
%K secure domination number
%K perfect secure domination number
%R
%X 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 $v$ 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 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.
%U http://cgasa.sbu.ac.ir/article_44926_4a0432bd29e2bbab421183f554f06243.pdf