Connectivity of consecutive-\(d\) digraphs
A consecutive-\(d\) digraph \(G(d,n,q,r)\) is a digraph with \(n (>d)\) nodes labeled by the residues modulo \(n\) and there exist links from \(i\) to \(j\) iff \(j\equiv qi+r,\dots,qi+r+d-1\pmod n\) for some given \(q\) and \(r\), \(q\neq 0\). This concept generalizes the class of generalized De Bruijn digraphs (see, i.e., \textit{D. Z. Du} and \textit{F. K. Hwang} [Networks 18, No. 1, 27-38 (1988; Zbl 0654.05036)]). The authors prove that if a consecutive-\(d\) digraph is modified by connecting nodes with a loop into a circuit and deleting all loops then the link-connectivity of such a graph is \(d\) \((d>2)\) iff \(\text{gcd}(q,n)\) divides \(d\).
scientific article; zbMATH DE number 94306
scientific article