• THE EQUITABLE BONDAGE NUMBER OF A GRAPH

G. Deepak, N. D. Soner, Anwar Alwardi*

Abstract


A subset D of V is called an equitable dominating set if for every v  V – D there exists a vertex u  D such that uv  E(G) and |deg(u) – deg(v)| 1. The minimum cardinality of such a dominating set is called the equitable domination number and is denoted by e(G). We define the equitable bondage number be(G) of a graph G to be the cardinality of a smallest set X  E of edges for which e(G – X) > e(G). Sharp bounds are obtained for be(G) and the exact values are determined for some standard graphs.

Keywords: Graph, Bondage number, Equitable bondage number, Equitable domination number, Equitable domination.

Mathematics Subject Classification : 05C70.

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