Details
| Original language | English |
|---|---|
| Article number | 113467 |
| Journal | Discrete Mathematics |
| Volume | 346 |
| Issue number | 8 |
| Early online date | 20 Apr 2023 |
| Publication status | Published - Aug 2023 |
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.
Keywords
- math.CO, math.GR, 05C25, Non-solvable group, Graph, Clique number, Conjugacy class
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Discrete Mathematics, Vol. 346, No. 8, 113467, 08.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Solvable conjugacy class graph of groups
AU - Bhowal, Parthajit
AU - Cameron, Peter J.
AU - Nath, Rajat Kanti
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2023 The Author(s)
PY - 2023/8
Y1 - 2023/8
N2 - 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.
AB - 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.
KW - math.CO
KW - math.GR
KW - 05C25
KW - Non-solvable group
KW - Graph
KW - Clique number
KW - Conjugacy class
UR - http://www.scopus.com/inward/record.url?scp=85152964855&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2023.113467
DO - 10.1016/j.disc.2023.113467
M3 - Article
VL - 346
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 8
M1 - 113467
ER -