On Frobenius graphs of diameter 3 for finite groups

TL;DR

This paper studies Frobenius graphs derived from finite groups, focusing on conditions under which these graphs have diameter 3, thereby linking group theory with graph properties.

Contribution

It characterizes when Frobenius graphs of finite groups have diameter 3, providing new insights into their structure and properties.

Findings

Identifies conditions for Frobenius graphs to have diameter 3

Establishes connections between group characters and graph diameter

Provides classifications for specific group-subgroup pairs

Abstract

For a subgroup $H$ of a finite group $G$, the Frobenius graph $\Gamma(G, H)$ records the constituents of the restrictions to $H$ of the irreducible characters of $G$. We investigate when this graph has diameter 3.