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Super line-connectivity of consecutive-\(d\) digraphs. (English) Zbl 0895.05035
D.-Z. Du, D. F. Hsu and F. K. Hwang [Math. Comput. Modelling 17, No. 11, 61-63 (1993; Zbl 0789.05040)] introduced the concept of consecutive-\(d\) digraphs. A consecutive-\(d\) digraph \(G(d,n,q,r)\) has \(n\) nodes, labeled by integers \(\bmod n\), with edges from each node \(i\) to \(d\) consecutive nodes, namely those with label \(qi+r+k \pmod n\) for \(0\leq k<d \leq n\), where \(r\) and \(q\) are integers and \(-n/2<q \leq n/2\), \(q\neq 0\).
A digraph is called a modified \(G(d,n,q,r)\) if it is constructed from \(G(d,n,q,r)\) by connecting all loop-nodes into disjoint cycles of cardinality at least two and deleting all loops. Also a digraph is said to have super line-connectivity if its line-connectivity equals the minimum degree and every minimum edge-cut consists of edges incident to the same node. The authors give sufficient conditions for modified consecutive-\(d\) digraphs to have super line-connectivity.
Reviewer: M.Hager (Leonberg)

05C40 Connectivity
05C20 Directed graphs (digraphs), tournaments
Full Text: DOI
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