Graphs and Combinatorics

, Volume 33, Issue 2, pp 485–487 | Cite as

Coloring the Power Graph of a Semigroup

  • Yaroslav Shitov
Original Paper


Let G be a semigroup. The vertices of the power graph \({\mathcal {P}}(G)\) are the elements of G, and two elements are adjacent if and only if one of them is a power of the other. We show that the chromatic number of \({\mathcal {P}}(G)\) is at most countable, answering a recent question of Aalipour et al.


Power graph Chromatic number 

Mathematics Subject Classification

05C15 20F99 


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Copyright information

© Springer Japan 2017

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

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