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Two lower bounds for generalized 3-connectivity of Cartesian product graphs

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  • Gao, Hui
  • Lv, Benjian
  • Wang, Kaishun

Abstract

The generalized k-connectivity κk(G) of a graph G, which was introduced by Chartrand et al. (1984) is a generalization of the concept of vertex connectivity. Let G and H be nontrivial connected graphs. Recently, Li et al. (2012) gave a lower bound for the generalized 3-connectivity of the Cartesian product graph G□H and proposed a conjecture for the case that H is 3-connected. In this paper, we give two different forms of lower bounds for the generalized 3-connectivity of Cartesian product graphs. The first lower bound is stronger than theirs, and the second confirms their conjecture.

Suggested Citation

  • Gao, Hui & Lv, Benjian & Wang, Kaishun, 2018. "Two lower bounds for generalized 3-connectivity of Cartesian product graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 305-313.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:305-313
    DOI: 10.1016/j.amc.2018.04.007
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    References listed on IDEAS

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    1. Shasha Li & Xueliang Li, 2012. "Note on the hardness of generalized connectivity," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 389-396, October.
    2. Li, Shasha & Tu, Jianhua & Yu, Chenyan, 2016. "The generalized 3-connectivity of star graphs and bubble-sort graphs," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 41-46.
    3. Li, Hengzhe & Ma, Yingbin & Yang, Weihua & Wang, Yifei, 2017. "The generalized 3-connectivity of graph products," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 77-83.
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