This article computes genus of commuting graphs in finite non-abelian groups, characterizing specific groups geometrically.
The commuting graph of a finite group G is a graph whose vertex set is the set of non-central elements of G and two distinct vertices are adjacent if they commute. In this article, we compute genus of commuting graphs of certain classes of finite non-abelian groups and characterize those groups such that their commuting graphs have genus 4, 5 and 6.
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Bhowal et al. (2025) studied this question.
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