Solvable conjugacy class graph of groups

Parthajit Bhowal, Peter J. Cameron*, Rajat Kanti Nath, Benjamin Sambale

*Corresponding author for this work

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In this paper we introduce the graph Γsc(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 and y generate a solvable group.

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.
Original languageEnglish
Article number113467
Number of pages8
JournalDiscrete Mathematics
Issue number8
Early online date20 Apr 2023
Publication statusPublished - 1 Aug 2023


  • Clique number
  • Non-solvable group
  • Graph
  • Girth
  • Conjugacy class


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