TY - JOUR
ID - 44926
TI - Perfect secure domination in graphs
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Rashmi, S.V. Divya
AU - Arumugam, Subramanian
AU - Bhutani, Kiran R.
AU - Gartland, Peter
AD - Department of Mathematics, Vidyavardhaka College of Engineering, Mysuru 570002, Karnataka, India.
AD - National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University, Anand Nagar, Krishnankoil-626 126, Tamil Nadu, India.
AD - Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, USA.
Y1 - 2017
PY - 2017
VL - 7
IS - Special Issue on the Occasion of Banaschewski's 90th Birthday (II)
SP - 125
EP - 140
KW - Secure domination
KW - perfect secure domination
KW - secure domination number
KW - perfect secure domination number
DO -
N2 - 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.
UR - http://cgasa.sbu.ac.ir/article_44926.html
L1 - http://cgasa.sbu.ac.ir/article_44926_4a0432bd29e2bbab421183f554f06243.pdf
ER -