SUBDIVISION NUMBER OF SPLIT POINT SET DOMINATION OF A GRAPH

Abstract

Let G= (V,E) be a connected, nontrivial, simple, finite graph. In this paper a new parameter called subdivision split point set domination is introduced and is defined by a set D of vertices in a graph G is a subdivision point set domination, if (i) The graph obtained from a graph G by subdividing each edge of G exactly once (ii) For every set S⊆ V-D such that v∈ D, that is <S ∪ {v}> is connected. (iii) The induced sub graph <V-D> is disconnected.The minimum cardinality of subdivision split point set dominating set is denoted by sp (S (G)). Besides some bounds, exact values of sp(S (G)) are determined. Some theorems based on split point Set Domination are also discussed.