Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58537Special Issue on the Occasion of Banaschewski's 90th Birthday (II)20170701Perfect secure domination in graphs12514044926ENS.V. DivyaRashmiDepartment of Mathematics, Vidyavardhaka College of Engineering, Mysuru 570002, Karnataka, India.SubramanianArumugamNational Centre for Advanced Research in Discrete Mathematics, Kalasalingam University, Anand Nagar, Krishnankoil-626 126, Tamil Nadu, India.Kiran R.BhutaniDepartment of Mathematics, The Catholic University of America, Washington, D.C. 20064, USA.PeterGartlandDepartment of Mathematics, The Catholic University of America, Washington, D.C. 20064, USA.Journal Article20161016Let $G=(V,E)$ 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.http://cgasa.sbu.ac.ir/article_44926_4a0432bd29e2bbab421183f554f06243.pdf