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The Rainbow Connection Number of the Power Graph of a Finite Group
Authors:Xuanlong Ma  Min Feng  Kaishun Wang
Institution:1.Sch. Math. Sci. and Lab. Math. Com. Sys.,Beijing Normal University,Beijing,China;2.Department of Applied Mathematics,Nanjing University of Science and Technology,Nanjing,China
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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