Split bondage numbers of a graph

Abstract

Let G = (V, E) be a graph. The negative split bondage number of G is the minimum cardinality among all sets of edges X ? E such that ?s (G ? S) < ?s (G) and the split bondage number bs (G) of G is the minimum cardinality among all sets of edges X ? E such that ?s (G ? X) > ?s (G), where ?s (G) is the split domination number of G. In this paper, we initiate a study of these two new parameters. © 1998 Taylor & Francis Group, LLC.