Bondage number of planar graphs without small cycles

Abstract

The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than γ(G), where γ(G) denotes the domination number of G. Let G be a connected planar graph. In this paper, we shall show that if G is free of i-cycles for some i ε {3,4,5,6}, then b(G) ≤ 6.