A survey on conjugacy class graphs of groups
Abstract
There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group G and adjacency is defined by properties of the elements of conjugacy classes. In particular, we consider commuting/nilpotent/solvable conjugacy class graph of G where two distinct onjugacy classes aG and bG are adjacent if there exist some elements x ∈ aG and y ∈ bG such that ⟨x y⟩ is abelian/nilpotent/solvable. After a section of introductory results and examples, we discuss all the available results on connectedness, graph realization, genus, various spectra and energies of certain induced subgraphs of these graphs. Proofs of the results are not included. However, many open problems for further investigation are stated.
Citation
Cameron , P J , Jannat , F E , Nath , R K & Sharafdini , R 2024 , ' A survey on conjugacy class graphs of groups ' , Expositiones Mathematicae , vol. 42 , no. 4 , 125585 . https://doi.org/10.1016/j.exmath.2024.125585
Publication
Expositiones Mathematicae
Status
Peer reviewed
ISSN
0723-0869Type
Journal article
Description
Funding: F. E. Jannat would like to thank DST for the INSPIRE Fellowship (IF200226).Collections
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