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Solvable conjugacy class graph of groups.
- Source :
-
Discrete Mathematics . Aug2023, Vol. 346 Issue 8, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- In this paper we introduce the graph Γ s c (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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CONJUGACY classes
*FINITE groups
*LIBRARY catalogs
Subjects
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 346
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 163931672
- Full Text :
- https://doi.org/10.1016/j.disc.2023.113467