Solvable conjugacy class graph of groups

In this paper we introduce the graph Gamma(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 is an element of C and y is an element of 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. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).