SEMIGLOBAL TOTAL DOMINATION IN GRAPHS

Abstract

A subset D of vertices of a connected graph G is called a semiglobal total dominating set if D is a dominating set for G and G sc and has no isolated vertex in G, where G sc is the semi complementary graph of G. The semiglobal total domination number is the minimum cardinality of a semiglobal total dominating set of G and is denoted by γ sgt (G). In this paper exact values for γ sgt (G) are obtained for some graphs like cycles, wheel and paths are presented as well.