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Exact assessment of the super \(P_k\)-connectivity for the crossed cube interconnection network

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Abstract

A network is connected if there exists a path between any two distinct vertices. The vertex-connectivity of any connected network is the cardinality of its minimum vertex-cut. Then, a network is super connected if every of its minimum vertex-cuts always consists of a certain vertex’s neighborhood. Kung and Lin (Discret Appl Math 293: 143–156, 2021) recently defined the notion of the super cluster-connectivity as a novel, generalized measure to quantify a network’s connectedness level. This article is dedicated to establishing a deep analysis on the exact formula of super path-connectivity for the crossed cube interconnection network. Accordingly, a sufficient and necessary condition is presented to classify whether or not crossed cubes can be super path-connected.

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Acknowledgements

This work is supported in part by the Ministry of Science and Technology, Taiwan, under Grant No. MOST 109-2221-E-468-009-MY2. The author would like to express the most immense gratitude to the anonymous referees and the editor for their constructive suggestions and efforts in improving the quality of this article.

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  1. Department of Computer Science and Information Engineering, Asia University, No. 500, Liufeng Rd., Taichung City, 41354, Taiwan, ROC

    Tzu-Liang Kung

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  1. Tzu-Liang Kung
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Correspondence to Tzu-Liang Kung.

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Kung, TL. Exact assessment of the super \(P_k\)-connectivity for the crossed cube interconnection network. J Supercomput 78, 15857–15881 (2022). https://doi.org/10.1007/s11227-022-04494-4

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