Walk Regular Digraphs

Wen Liu1, Jing Lin2
1Math. & Inf. College, Hebei Normal University, Shijiazhuang, 050016, China
2Beijing Daxing No.5 High School, Beijing, 102600, China

Abstract

A strongly connected digraph \(\Gamma\) is said to be walk regular if for any nonnegative integer \(l\) and any vertex \(u\) of \(\Gamma\), the number of circuits of length \(l\) containing \(u\) depends only on \(l\). This family of digraphs is a directed version of walk regular graphs. In this paper, we discuss some basic properties of walk regular digraphs.