Publication details
Solvable conjugacy class graph of groups
Abstract
In this paper we introduce the graph Γ
sc(G) associated with a group G, called the solvable conjugacy class graph (abbreviated as SCC-graph), whose vertices are the nontrivial conjugacy classes of G and two distinct conjugacy classes C,D are adjacent if there exist x∈C and y∈D such that 〈x,y〉 is solvable. We discuss the connectivity, girth, clique number, and several other properties of the SCC-graph. One of our results asserts that there are only finitely many finite groups whose SCC-graph has given clique number d, and we find explicitly the list of such groups with d=2. We pose some problems on the relation of the SCC-graph to the solvable graph and to the NCC-graph, which we cannot solve.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- External Organisation(s)
-
Tezpur University
University of St. Andrews
- Type
- Article
- Journal
- Discrete Mathematics
- Volume
- 346
- ISSN
- 0012-365X
- Publication date
- 08.2023
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Theoretical Computer Science, Discrete Mathematics and Combinatorics
- Electronic version(s)
-
https://doi.org/10.1016/j.disc.2023.113467 (Access:
Open
)
https://doi.org/10.48550/arXiv.2112.02613 (Access: Open )
