Schwarz, Štefan Common consequents in directed graphs. (English) Zbl 0575.05041 Czech. Math. J. 35(110), 212-247 (1985). If u and v are two distinct nodes of a directed graph \(G_ n\), let N(u,v) denote the least integer k (if it exists) such that there exists a node w whose distance from u and whose distance from v equals k. The author shows that if N(u,v) exists then N(u,v)\(\leq [(n^ 2+3)/2]-n\). Reviewer: J.W.Moon Cited in 5 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C38 Paths and cycles 05C20 Directed graphs (digraphs), tournaments Keywords:Boolean matrices; path lengths; directed graph × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Paz A.: Introduction to probabilistic automata. Academic Press, New York, 1971. · Zbl 0234.94055 [2] Schwarz Š.: On the semigroup of binary relations on a finite set. Czech. Math. J. 20 (1970), 632-679. · Zbl 0228.20034 [3] Schwarz Š.: On a sharp estimation in the theory of binary relations on a finite set. Czech. Math. J. 20 (1970), 703-714. · Zbl 0226.20061 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.