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Generalized 4-connectivity of alternating group networks

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Abstract

Connectivity is a fundamental attribute crucial for the efficiency of interconnection networks, especially in domains requiring robust communication infrastructures. A natural generalization of the connectivity is the generalized connectivity introduced by Hager (J Combin Theory Ser B 38:179–189, 1985). This paper explores the problem of determining the generalized 4-connectivity of the alternating group network (\(AN_n\)), motivated by the challenges inherent in designing resilient and efficient networks. We prove that for any set of four vertices in \(AN_n\), there exist \(n-2\) trees in \(AN_n\) having in common exactly these four vertices, offering insights into the network’s structural characteristics with implications for applications demanding resilient communication paths. Additionally, we establish the value of the generalized 4-edge-connectivity of \(AN_n\).

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Acknowledgements

I want to thank the reviewers for their helpful comments and suggestions, which greatly improved this paper. Their valuable feedback played a crucial role in shaping the final version.

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  1. Department of Mathematics and Natural Sciences, American University of Kuwait, Salem Al Mubarak St., Salmiya, Kuwait

    Mohamad Abdallah

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  1. Mohamad Abdallah
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Correspondence to Mohamad Abdallah.

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Abdallah, M. Generalized 4-connectivity of alternating group networks. J Supercomput 80, 12585–12598 (2024). https://doi.org/10.1007/s11227-024-05922-3

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