Solvable conjugacy class graph of groups

In this paper we introduce the graph Γsc(G) associated with a group G, called solvable conjugacy class (abbreviated as SCC-graph), whose vertices are nontrivial classes of G and two distinct C,D adjacent if there exist x∈C y∈D such that 〈x,y〉 is solvable. We discuss connectivity, girth, clique number, several other properties SCC-graph. One our results asserts only finitely many finite groups SCC-graph has given number d, find explicitly list d=2. pose some problems on relation to NCC-graph, which cannot solve.