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The Rainbow Connection Number of the Power Graph of a Finite Group

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Abstract

This paper studies the rainbow connection number of the power graph \(\Gamma _G\) of a finite group G. We determine the rainbow connection number of \(\Gamma _G\) if G has maximal involutions or is nilpotent, and show that the rainbow connection number of \(\Gamma _G\) is at most three if G has no maximal involutions. The rainbow connection numbers of power graphs of some nonnilpotent groups are also given.

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Acknowledgments

The authors are grateful to the referees for many useful suggestions and comments. This research is supported by National Natural Science Foundation of China (11271047, 11371204) and the Fundamental Research Funds for the Central University of China.

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Authors and Affiliations

  1. Sch. Math. Sci. and Lab. Math. Com. Sys., Beijing Normal University, Beijing, 100875, China

    Xuanlong Ma & Kaishun Wang

  2. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, China

    Min Feng

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  1. Xuanlong Ma
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  2. Min Feng
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Correspondence to Xuanlong Ma.

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Ma, X., Feng, M. & Wang, K. The Rainbow Connection Number of the Power Graph of a Finite Group. Graphs and Combinatorics 32, 1495–1504 (2016). https://doi.org/10.1007/s00373-015-1665-8

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  • DOI: https://doi.org/10.1007/s00373-015-1665-8

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