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Recognizing the Commuting Graph of a Finite Group

Published 2 Jun 2022 in math.GR and cs.CC | (2206.01059v1)

Abstract: In this paper we study the realizability question for commuting graphs of finite groups: Given an undirected graph $X$ is it the commuting graph of a group $G$? And if so, to determine such a group. We seek efficient algorithms for this problem. We make some general observations on this problem, and obtain a polynomial-time algorithm for the case of extraspecial groups.

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