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The antipodal graph of a graph G, denoted by A(G), has the same vertex setas G with an edge joining vertices u and v if d(u,v) is equal to the diameter of G. (If G isdisconnected, 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 anantipodal digraph if and only if D is the antipodal digraph of its complement. This generalizesa known characterization for antipodal graphs and provides an improved proof. Examplesand properties of antipodal digraphs are given. A digraph D is self-antipodal if A(D) isisomorphic to D. Several characteristics of a self-antipodal digraph D are given includingsharp upper and lower bounds on the size of D. Similar results are given for self-antipodalgraphs

Antipodal graphs and digraphs