A sufficient condition for equality of arc-connectivity and minimum degree of a digraph
type: Item
instance of: scholarly article
title: A sufficient condition for equality of arc-connectivity and minimum degree of a digraph
zbMATH Open document ID: 0808.05068
DOI: 10.1016/0012-365X(94)90040-X
published in: Discrete Mathematics
publication date: 1995-03-09T00:00:00Z
review text: Let \(D\) be a simple digraph of order \(p\). For \(v \in V (D)\), \(d_ D (v)\) is the minimum of the in-degree and the out-degree of \(v\), and \(\delta (D)\) is the minimum \(d_ D (v)\), over all \(v\). The strong arc- connectivity of \(D\) is denoted by \(\lambda(D)\). It is shown that if there are \(\lfloor p/2\rfloor\) pairs of vertices \(u_ i\), \(v_ i\) of \(D\) such that \(d_ D (u_ i) + d_ D (v_ i) \geq p\), for \(i = 1, 2, \dots , \lfloor p/2 \rfloor\), then \(\lambda (D) = \delta (D)\). This generalizes a theorem of \textit{D. L. Goldsmith} and the reviewer [Discrete Math. 23, 31- 36 (1978; Zbl 0393.05035)] for simple graphs.
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 681712
zbMATH Keywords: simple digraph
zbMATH Keywords: in-degree
zbMATH Keywords: out-degree
zbMATH Keywords: strong arc-connectivity
author: Jun-Ming Xu
reviewed by: Arthur T. White
MaRDI profile type: Publication
cites work: On graphs with equal edge-connectivity and minimum degree
full work available at URL: 0012-365x(94)90040-x
OpenAlex ID: W2050192535
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description: scientific article; zbMATH DE number 681712