Article ID Journal Published Year Pages File Type
4672802 Indagationes Mathematicae 2015 8 Pages PDF
Abstract

The power graph ΓGΓG of a finite group GG is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. We investigate the chromatic number χ(ΓG)χ(ΓG) of ΓGΓG. A characterization of χ(ΓG)χ(ΓG) is presented, and a conjecture in Mirzargar et al. (2012) is disproved. Moreover, we classify all finite groups whose power graphs are uniquely colorable, split or unicyclic.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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