Groups whose character degree graph has diameter three

Let $G$ be a finite group, and let $Δ(G)$ denote the \emph{prime graph} built on the set of degrees of the irreducible complex characters of $G$. It is well known that, whenever $Δ(G)$ is connected, the diameter of $Δ(G)$ is at most $3$. In the present paper, we provide a description of the finite solvable groups for which the diameter of this graph attains the upper bound. This also enables us to confirm a couple of conjectures proposed by M.L. Lewis.

No reviews yet.

No comments yet.