SET DOMINATION MAXSUBDIVISION NUMBER OF GRAPHS

Abstract

Let G=(V,E) be a simple, undirected, finite nontrivial graph. A non empty set SV of vertices in a graph G is called a dominating set if every vertex in V-S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G.A dominating set S is a set dominating set of G if for every set TV-S , there exists a non-empty set RS such that the subgraph <RUT> is connected. The set domination number of G is the minimum cardinality of a set dominating set of G and it is denoted by γs (G).The set domination maxsubdivision number of G is the maximum number of edges that must be subdivided (where each edge in G can be subdivided atmost once) in order to increase the set domination number and is denoted by msdγs(G). In this paper, we establish the properties and exact values of the set domination maxsubdivision number for some families of graphs.