Leonard, Douglas A.; Nomura, Kazumasa The girth of a directed distance-regular graph. (English) Zbl 0733.05044 J. Comb. Theory, Ser. B 58, No. 1, 34-39 (1993). Summary: Let \(G=(V,E)\) be a connected digraph with the usual (non-symmetric) metric \(\partial\). For u,v\(\in V\), let \[ p_{ij}(u,v)=\#\{w\in V:\;\partial (u,w)=i,\quad \partial (w,v)=j\}. \] G is said to be distance- regular if \(\partial (u,v)=\partial (u',v')\) implies \(p_{i,j}(u,v)=p_{i,j}(u',v')\) for all i, j. In this article, it is shown that if G is a directed distance-regular graph (other than a directed cycle or its coclique extension), then G has girth \(g\leq 8\). Cited in 6 Documents MSC: 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles 05C12 Distance in graphs Keywords:digraph; directed distance-regular graph; girth PDFBibTeX XMLCite \textit{D. A. Leonard} and \textit{K. Nomura}, J. Comb. Theory, Ser. B 58, No. 1, 34--39 (1992; Zbl 0733.05044) Full Text: DOI