Elsevier

Discrete Applied Mathematics

Volume 230, 30 October 2017, Pages 133-145
Discrete Applied Mathematics

Bondage number of the strong product of two trees

https://doi.org/10.1016/j.dam.2017.06.019Get rights and content
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Abstract

The bondage number b(G) of a nonempty graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with domination number greater than that of G. It is known that b(T)2 for any nontrivial tree T. In this paper, we obtain that the bondage number of the strong product of two nontrivial trees b(TT) is equal to b(T)b(T) or b(T)b(T)+1, which implies that b(TT) is equal to 1, 2, 3, 4 or 5.

Keywords

Bondage number
Strong product
Trees

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This work is supported by NSFC (Grant Nos. 61501208, 11501282 & 11571155); Scientific Research Foundation of Jianghan University (No. 1019-06240001).