1-Connected character-graphs of finite groups with non-bipartite complement

Abstract

For a finite group G, let Δ(G) be the character-graph which is built on the set of irreducible complex character degrees of G. In this paper, we wish to determine the structure of finite groups G such that Δ(G) is 1-connected with nonbipartite complement. Also, we classify all 1-connected graphs with nonbipartite complement that can occur as the character-graph Δ(G) of a finite group G. © 2021 World Scientific Publishing Company.