Genus of commuting conjugacy class graph of groups
Parthajit Bhowal, Rajat Kanti Nath

TL;DR
This paper calculates the genus of the commuting conjugacy class graph for six well-known non-abelian two-generated groups, classifying their graphs as planar, toroidal, or higher genus surfaces.
Contribution
It provides explicit genus calculations for the commuting conjugacy class graphs of six specific classes of non-abelian groups, extending understanding of their topological properties.
Findings
Computed genus for each group class.
Classified graphs as planar, toroidal, or higher genus.
Identified topological types of these graphs.
Abstract
For a non-abelian group , its commuting conjugacy class graph is a simple undirected graph whose vertex set is the set of conjugacy classes of the non-central elements of and two distinct vertices and are adjacent if there exists some elements and such that . In this paper we compute the genus of for six well-known classes of non-abelian two-generated groups (viz. and ) and determine whether for these groups are planar, toroidal, double-toroidal or triple-toroidal.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · Geometric and Algebraic Topology
