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.
Citation
Wen Liu, Jing Lin. Walk Regular Digraphs[J], Ars Combinatoria, Volume 095. 97-102. .