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.
Original language | English |
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Article number | 125585 |
Journal | Expositiones Mathematicae |
Volume | 42 |
Issue number | 4 |
Early online date | 11 Jun 2024 |
DOIs | |
Publication status | Published - Jul 2024 |
Keywords
- Commuting/nilpotent/solvable conjugacy class graph
- Connectedness
- Genus
- Spectrum and energy
- Induced subgraph