Character graphs with diameter three

Abstract

For a finite group $G$, let $\Delta (G)$ denote the character graph built on the set of degrees of the irreducible complex characters of $G$. In this paper, we show that if the diameter of $\Delta (G)$ is equal to three, then the complement of $\Delta (G)$ is bipartite. Also in this case, we determine the structure of the character graph $\Delta (G)$.

arXiv admin note: substantial text overlap with arXiv:1909.01180; text overlap with arXiv:1907.13292