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Characterizing finite nilpotent groups associated with a graph theoretic equality

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Abstract

The power graph of a group is the simple graph whose vertices are the group elements and two vertices are adjacent whenever one of them is a positive power of the other. In this paper, we characterize the finite nilpotent groups whose power graphs have equal vertex connectivity and minimum degree.

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Acknowledgements

The first author would like to thank the National Institute of Science Education and Research, Bhubaneswar, for the facilities provided when working as a visiting fellow in the School of Mathematical Sciences.

Funding

The third author is partially supported by Project No. MTR/2017/000372 of the Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India.

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Correspondence to Ramesh Prasad Panda.

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Panda, R.P., Patra, K.L. & Sahoo, B.K. Characterizing finite nilpotent groups associated with a graph theoretic equality. Ricerche mat 73, 1017–1027 (2024). https://doi.org/10.1007/s11587-021-00655-4

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  • DOI: https://doi.org/10.1007/s11587-021-00655-4

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