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Antipodal graphs and digraphs

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  • Garry Johns
  • Karen Sleno

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.

Suggested Citation

  • Garry Johns & Karen Sleno, 1993. "Antipodal graphs and digraphs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:205867
    DOI: 10.1155/S0161171293000717
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    Cited by:

    1. Kshittiz Chettri & Biswajit Deb, 2023. "On Characterization of Balance and Consistency Preserving d -Antipodal Signed Graphs," Mathematics, MDPI, vol. 11(13), pages 1-15, July.

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