A Bound on the bondage Number of toroidal Graphs

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.

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