Exact Pendant Domination in Graphs

Abstract

Let   be any graph. A dominating set   in   is said to be an Exact dominating set if for every vertex   is adjacent to exactly one vertex of  and for   is either adjacent to exactly one vertex of   or   is an isolate of  . That is,   for every   and and   for every   The least cardinality of an exact dominating set in   is called exact domination number, denoted by   A dominating set  in   is called a pendant dominating set if induced sub graph of  contains at least one pendant vertex. The least cardinality of a pendant dominating set in   is called the pendant domination number of  , denoted by  . In this article, we study the exact pendant domination number for path, Complete bipartite graph, Ladder graph, Pan graph, Double star graph, Diamond graph, Fish graph and also bounds for Exact pendant domination number.