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Bondage number of mesh networks

Frontiers of Mathematics in China volume 7, pages 813–826 (2012)Cite this article

Abstract

The bondage number b(G) of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with domination number greater than that of G. Denote P n × P m the Cartesian product of two paths P n and P m . This paper determines the exact values of b(P n × P 2), b(P n × P 3), and b(P n × P 4) for n ⩾ 2.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Beijing, China

    Futao Hu & Jun-Ming Xu

  2. Wentsun Wu Key Laboratory of Chinese Academy of Sciences, Hefei, 230026, China

    Futao Hu & Jun-Ming Xu

Authors
  1. Futao Hu
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  2. Jun-Ming Xu
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Correspondence to Jun-Ming Xu.

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Hu, F., Xu, JM. Bondage number of mesh networks. Front. Math. China 7, 813–826 (2012). https://doi.org/10.1007/s11464-012-0173-x

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  • DOI: https://doi.org/10.1007/s11464-012-0173-x

Keywords

  • Bondage number
  • dominating set
  • domination number
  • mesh network

MSC

  • 05C25
  • 05C40
  • 05C12
  • 05C69