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

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. [ABSTRACT FROM AUTHOR]