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A BOUND ON THE BONDAGE NUMBER OF TOROIDAL GRAPHS
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) denote the domination number of G. Let G be a toroidal graph with maximum degree Δ(G). In this paper, we show that b(G) ≤ 9. Moveover, if Δ(G) ≠ 6, then b(G) ≤ 8.
This work is supported by research grants NSFC (11001055, 60672030) and NSFFP (2010J05004, 2011J06001).
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