A NOTE ON SPLIT SET DOMINATION

Abstract

Let G=(V,E) be a simple, undirected, finite nontrivial graph. A non empty set S of V of vertices in a graph G is calleda dominating set if every vertex in V-S is adjacent to some vertex in S. The domination number γ(G) is theminimum cardinality of a dominating set of G.A dominating set S is called a non split set dominatingset if thereexists a non empty set R of S such that <RUT> is connected for every set T of V-Sand the induced subgraph<V-S>is not connected. The minimum cardinality of a split set dominating set is called the split set domination numberof G and is denoted by γss(G). In this paper, bounds for γss(G) andvalues for some particular classes of graphs are found and also the split set domination number of some standard graphs is given in this paper