PERFECT PENDANT DOMINATION IN GRAPHS

Abstract

Let G=(V(G),E(G)) be a simple connected graph. A set S\subseteq V(G) is said to be a perfect pendant dominating set of G if S is a perfect dominating set and pendant dominating set of G. The minimum cardinality of a perfect pendant dominating set of G is called perfect pendant domination number, and is denoted by \gamma_{ppe}(G). A perfect pendant dominating set S with |S|=\gamma_{ppe}(G) is said to be \gamma_{ppe}-set. In this paper we give a characterization of perfect pendant dominating set of some graphs and graphs obtained from the join and corona product of two graphs. Moreover, the perfect pendant domination number of the forenamed graphs is determined and also, graphs having no perfect pendant dominating set are examined.