Antipodal graphs and digraphs
type: Item
instance of: scholarly article
title: Antipodal graphs and digraphs
zbMATH Open document ID: 0783.05045
DOI: 10.1155/S0161171293000717
author: Karen Sleno
author: Garry Johns
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1994-03-13T00:00:00Z
full work available at URL: https://eudml.org/doc/46914
review text: To a given graph \(G\) we can define the antipodal graph \(A(G)\) which has the same vertex set as \(G\) and an edge \((u,v)\) is in \(A(G)\) if \(d(u,v)\) is equal to the diameter of \(G\). (If \(G\) is disconnected, then diam \(G=\infty.)\) This definition is extended to a digraph too. It is shown that a digraph \(D\) is an antipodal digraph if and only if \(D\) is the antipodal digraph of its complement. This result generalizes a known characterization of antipodal graphs. Authors also study self-antipodal digraphs (i.e. \(A(D)\) is isomorphic to \(D)\) and self-antipodal graphs. They give some interesting results. Note that in the literature other graphs were also called antipodal graphs, see e.g. \textit{A. Berman} and \textit{A. Kotzig} [Discrete Math. 69, No. 2, 107-114 (1988; Zbl 0667.05048)], \textit{A. Berman}, \textit{A. Kotzig} and \textit{G. Sabidussi} [Contemporary methods in graph theory. In honour of Prof. Dr. K. Wagner, 137-150 (1990; Zbl 0722.05042)] and \textit{K. Fukuda} and \textit{K. Handa} [Discrete Math. 111, No. 1-3, 245-256 (1993; Zbl 0782.05067)].
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 436741
zbMATH Keywords: antipodal graph
zbMATH Keywords: antipodal digraph
reviewed by: Ferdinand Gliviak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 436741