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

Abstract

For a finite group [Formula: see text], let [Formula: see text] be the character-graph which is built on the set of irreducible complex character degrees of [Formula: see text]. In this paper, we wish to determine the structure of finite groups [Formula: see text] such that [Formula: see text] is [Formula: see text]-connected with nonbipartite complement. Also, we classify all [Formula: see text]-connected graphs with nonbipartite complement that can occur as the character-graph [Formula: see text] of a finite group [Formula: see text].