Abstract
The bondage number b ( G ) of a nonempty graph G is defined to be the cardinality of the smallest set E of edges of G such that the graph G - E has domination number greater than that of G. In this paper we present a simple, intuitive proof that b ( G ) ⩽ min { 8 , Δ ( G ) + 2 } for all planar graphs G, give examples of planar graphs with bondage number 6, and bound the bondage number of directed graphs.
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