A Family of Tetravalent Frobenius Graphs

Abstract

As a part of the author’s work of enumerating the edge-forwarding indices of Frobenius graphs, I give a class of valency four Frobenius graphs derived from the Frobenius groups ${\mathbb{Z}}_{4n^2+1}⋊{\mathbb{Z}}_4$. Following the method of Fang, Li and Praeger, some properties including the diameter and the type of this class of graphs are given (Theorem $3.2$).