• SEMI GLOBAL DOMINATION

Abstract

A subset D of vertices of a graph connected graph G is called a semi global dominating set(sgd - set) iff D is a dominating set for both G and Gsc, where Gsc is the semi complementary graph of G. The semi global domination number (sgd - number) is the minimum cardinality of a semi global dominating set of G and is denoted by γsg (G). In this paper sharp bounds for γsg, are supplied for graphs whose girth is greater than three. Exact values of this number for paths and cycles are presented as well. The characterization result for a subset of the vertex set of G to be a semi global dominating set for G is given and also characterized the graphs of order n having sgd - numbers 2, n – 1, n.