Walk Regular Digraphs

Abstract

A strongly connected digraph $\mathrm{\Gamma }$ is said to be walk regular if for any nonnegative integer $l$ and any vertex $u$ of $\mathrm{\Gamma }$, 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.