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On the Connectivity of Enhanced Power Graphs of Finite Groups

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Abstract

This paper deals with the vertex connectivity of enhanced power graphs of finite groups. We classify all abelian groups G such that the vertex connectivity of enhanced power graph of G is 1. We derive an upper bound for the vertex connectivity of the enhanced power graph of any general abelian group G. Also we completely characterize all abelian groups G, such that the proper enhanced power graph is connected. Moreover, we study some special class of non-abelian groups G such that the proper enhanced power graph is connected and we find their vertex connectivity.

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Acknowledgements

The first author would like to thank Prof. Arvind Ayyer for his constant support and encouragement. The second author would like to thank Prof. Sivaramakrishnan Sivasubramanian for his constant support and encouragement. The third author would like to thank Prof. Basudeb Datta for his constant support and encouragement. The first author was supported by Department of Science and Technology Grant EMR/2016/006624 and partly supported by UGC Centre for Advanced Studies. Also the first author was supported by NBHM Post Doctoral Fellowship Grant 0204/52/2019/RD-II/339. The second author was supported by a CSIR-SPM fellowship. The third author was supported by NBHM Post Doctoral Fellowship Grant 0204/3/2020/RD-II/2470. The authors sincerely thank the anonymous referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    Sudip Bera & Sajal Kumar Mukherjee

  2. Department of Mathematics, Indian Institute of Technology, Bombay, India

    Hiranya Kishore Dey

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  1. Sudip Bera
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  2. Hiranya Kishore Dey
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  3. Sajal Kumar Mukherjee
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Bera, S., Dey, H.K. & Mukherjee, S.K. On the Connectivity of Enhanced Power Graphs of Finite Groups. Graphs and Combinatorics 37, 591–603 (2021). https://doi.org/10.1007/s00373-020-02267-5

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  • DOI: https://doi.org/10.1007/s00373-020-02267-5

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