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Bhowal, Parthajit; Cameron, Peter J.; Nath, Rajat Kanti; Sambale, Benjamin
Discrete mathematics, August 2023, 2023-08-00, Volume: 346, Issue: 8Journal Article
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,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.
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