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On the order supergraph of the power graph of a finite group

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Abstract

The power graph \({\mathcal {P}}_{G}\) of a finite group G is the graph whose vertex set is G, two distinct vertices are adjacent if one is a power of the other. The order supergraph \({\mathcal {S}}_{G}\) of \({\mathcal {P}}_G\) is the graph with vertex set G, and two distinct vertices x, y are adjacent if o(x)|o(y) or o(y)|o(x). In this paper, we study the independence number of \({\mathcal {S}}_{G}\) and answer a question was posed by Hamzeh and Ashrafi.

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Notes

  1. See http://www.planetmath.org/GeneralizedQuaternionGroup.

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Acknowledgements

We would like to thank the referee for a careful reading of the paper and for his/her valuable comments. This research was supported by the National Natural Science Foundation of China (Grant No. 11801441, Grant No. 11661013), the Natural Science Basic Research Program of Shaanxi (Program No. 2020JQ-761) and the Young Talent fund of University Association for Science and Technology in Shaanxi, China (Program No. 20190507).

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  1. School of Science, Xi’an Shiyou University, Xi’an, 710065, People’s Republic of China

    Xuanlong Ma

  2. School of Mathematics and Statistics, Nanning Normal University, Nanning, 530023, Guangxi, People’s Republic of China

    Huadong Su

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  1. Xuanlong Ma
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Ma, X., Su, H. On the order supergraph of the power graph of a finite group. Ricerche mat 71, 381–390 (2022). https://doi.org/10.1007/s11587-020-00520-w

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  • DOI: https://doi.org/10.1007/s11587-020-00520-w

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