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Integer k-matching preclusion of twisted cubes and (n,s)-star graphs

Author

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  • Chang, Caibing
  • Li, Xianfu
  • Liu, Yan

Abstract

An integer k-matching of a graph G is a function f from E(G) to {0,1,⋯,k} such that the sum of f(e) is not more than k for any vertex u, where the sum is taken over all edges e incident to u. When k=1, the integer k-matching is a matching. The (strong) integer k-matching preclusion number of G, denoted by mpk(G) (smpk(G)), is the minimum number of edges (vertices and edges) whose deletion results in a graph with neither perfect integer k-matching nor almost perfect integer k-matching. This is an extension of the (strong) matching preclusion problem that was introduced by Brigham, Park and Ihm et al. The twisted cubes and the (n,s)-star graphs have more desirable properties. In this paper, MPk number and SMPk number of the twisted cubes and (n,s)-star graphs are given, respectively.

Suggested Citation

  • Chang, Caibing & Li, Xianfu & Liu, Yan, 2023. "Integer k-matching preclusion of twisted cubes and (n,s)-star graphs," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s009630032200710x
    DOI: 10.1016/j.amc.2022.127638
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    References listed on IDEAS

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    1. Yan Liu & Weiwei Liu, 2017. "Fractional matching preclusion of graphs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 522-533, August.
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