Antipodal graphs and digraphs

Garry Johns and Karen Sleno

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-8

Abstract:

The antipodal graph of a graph G , denoted by A ( G ) , has the same vertex set as G with an edge joining vertices u and v if d ( u , v ) is equal to the diameter of G . (If G is disconnected, then diam G = ∞ .) This definition is extended to a digraph D where the arc ( u , v ) is included in A ( D ) if d ( u , v ) is the diameter of D . It is shown that a digraph D is an antipodal digraph if and only if D is the antipodal digraph of its complement. This generalizes a known characterization for antipodal graphs and provides an improved proof. Examples and properties of antipodal digraphs are given. A digraph D is self-antipodal if A ( D ) is isomorphic to D . Several characteristics of a self-antipodal digraph D are given including sharp upper and lower bounds on the size of D . Similar results are given for self-antipodal graphs.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:205867

DOI: 10.1155/S0161171293000717

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