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Neighbor Connectivity of Two Kinds of Cayley Graphs

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Abstract

In this paper, we determine the neighbor connectivity κNB of two kinds of Cayley graphs: alternating group networks AN n and star graphs S n ; and give the exact values of edge neighbor connectivity λNB of ANn and Cayley graphs generated by transposition trees Γ n . Those are κNB(AN n ) = n−1, λNB(AN n ) = n−2 and κNB(S n ) = λNB(Γ n ) = n−1.

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Acknowledgements

The authors thank the referees for many valuable suggestions such that the paper is improved in the survival version.

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Authors and Affiliations

  1. Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Yi-jie Shang, Rong-xia Hao & Mei-mei Gu

Authors
  1. Yi-jie Shang
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  2. Rong-xia Hao
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  3. Mei-mei Gu
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Corresponding author

Correspondence to Rong-xia Hao.

Additional information

Supported by the National Natural Science Foundation of China (No. 11371052, 11731002, 11571035).

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Shang, Yj., Hao, Rx. & Gu, Mm. Neighbor Connectivity of Two Kinds of Cayley Graphs. Acta Math. Appl. Sin. Engl. Ser. 34, 386–397 (2018). https://doi.org/10.1007/s10255-018-0739-9

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  • DOI: https://doi.org/10.1007/s10255-018-0739-9

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