A survey on conjugacy class graphs of groups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913271366287360 |
|---|---|
| author | Cameron, P. J. Jannat, F. E. Nath, R. K. Sharafdini, R. |
| author_facet | Cameron, P. J. Jannat, F. E. Nath, R. K. Sharafdini, R. |
| contents | 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 conjugacy classes $a^G$ and $b^G$ are adjacent if there exist some elements $x\in a^G$ and $y\in b^G$ such that $\langle x, y \rangle$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A survey on conjugacy class graphs of groups Cameron, P. J. Jannat, F. E. Nath, R. K. Sharafdini, R. Group Theory Combinatorics 05C25, 20D60 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 conjugacy classes $a^G$ and $b^G$ are adjacent if there exist some elements $x\in a^G$ and $y\in b^G$ such that $\langle x, y \rangle$ 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. |
| title | A survey on conjugacy class graphs of groups |
| topic | Group Theory Combinatorics 05C25, 20D60 |
| url | https://arxiv.org/abs/2403.09423 |