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Star structure connectivity of cayley graphs generated by transposition trees

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Abstract

To provide more accurate indicator for the fault-tolerance of networks, structure connectivity and substructure connectivity have been introduced. H-structure connectivity \(\kappa (G;H)\) is the minimum number of subgraphs isomorphic to H in G, such that the deletion of those subgraphs disconnects G. H-substructure connectivity \(\kappa ^s(G;H)\) is the minimum number of subgraphs isomorphic to connected subgraphs of H in G, such that the deletion of those subgraphs disconnects G. In this paper, we establish star structure and star substructure connectivity of Cayley graphs generated by transposition trees, which include bubble-sort graph and star graph.

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Acknowledgments

The authors would like to appreciate all anonymous reviewers for their insightful comments and constructive suggestions to polish this paper in high quality.

Funding

This article was completed during the period when the second author Dongqin Cheng was visiting Nanyang Technological University with financial support from China Scholarship Council (CSC No. 202006785015).

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Authors and Affiliations

  1. Department of Mathematics, College of Information Science and Technology / College of Cyberspace Security, Jinan University, Guangzhou, 510632, China

    Kaige Pan & Dongqin Cheng

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  1. Kaige Pan
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  2. Dongqin Cheng
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All authors contributed to the study conception and design. All authors read and approved the final manuscript.

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Correspondence to Dongqin Cheng.

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Pan, K., Cheng, D. Star structure connectivity of cayley graphs generated by transposition trees. J Supercomput 79, 4398–4411 (2023). https://doi.org/10.1007/s11227-022-04837-1

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