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The generalized connectivity of the line graph and the total graph for the complete bipartite graph

Author

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  • Li, Yinkui
  • Gu, Ruijuan
  • Lei, Hui

Abstract

The generalized k-connectivity κk(G) of a graph G, introduced by Hager (1985), is a natural generalization of the concept of connectivity κ(G), which is just for k=2. This parameter is often used to measure the capability of a network G to connect any k vertices in G. The line graph and the total graph are usually seen as important models for interconnection networks. In this paper, we determine the generalized 3-(edge-)connectivity of the line graph and the total graphs of the complete bipartite graph and discuss the bound for generalized 3-connectivity of the total graphs.

Suggested Citation

  • Li, Yinkui & Gu, Ruijuan & Lei, Hui, 2019. "The generalized connectivity of the line graph and the total graph for the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 645-652.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:645-652
    DOI: 10.1016/j.amc.2018.11.038
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    Cited by:

    1. Zhao, Shu-Li & Hao, Rong-Xia & Wei, Chao, 2022. "Internally disjoint trees in the line graph and total graph of the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Zhu, Wen-Han & Hao, Rong-Xia & Feng, Yan-Quan & Lee, Jaeun, 2023. "The 3-path-connectivity of the k-ary n-cube," Applied Mathematics and Computation, Elsevier, vol. 436(C).

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