Component connectivity of wheel networks

Guozhen Zhang, Xin Liu and Dajin Wang

Applied Mathematics and Computation, 2025, vol. 487, issue C

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.

Keywords: Interconnection networks; Reliability; Wheel networks; Component connectivity (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005575

DOI: 10.1016/j.amc.2024.129096

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