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Component connectivity of wheel networks

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  • Zhang, Guozhen
  • Liu, Xin
  • Wang, Dajin

Abstract

The r-component connectivity cκr(G) of a noncomplete graph G is the size of a minimum set of vertices, whose deletion disconnects G such that the remaining graph has at least r components. When r=2, cκr(G) is reduced to the classic notion of connectivity κ(G). So cκr(G) is a generalization of κ(G), and is therefore a more general and more precise measurement for the reliability of large interconnection networks. The m-dimensional wheel network CWm was first proposed by Shi and Lu in 2008 as a potential model for the interconnection network [19], and has been getting increasing attention recently. It belongs to the category of Cayley graphs, and possesses some properties desirable for interconnection networks. In this paper, we determine the r-component connectivity of the wheel network for r=3,4,5. We prove that cκ3(CWm)=4m−7 for m≥5, cκ4(CWm)=6m−13 and cκ5(CWm)=8m−20 for m≥6.

Suggested Citation

  • Zhang, Guozhen & Liu, Xin & Wang, Dajin, 2025. "Component connectivity of wheel networks," Applied Mathematics and Computation, Elsevier, vol. 487(C).
    • Handle: RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005575
    DOI: 10.1016/j.amc.2024.129096
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