Define an antipode of a given graph vertex as a vertex at greatest possible graph
distance from .
Then an antipodal graph is a connected graph in
which each vertex has exactly one antipode (Gorovoy and Zmiaikou 2021).

The numbers of antipodal graphs on , 2, ... nodes are 1, 1, 0, 2, 1, 5, 8, 73, 660, 9909, ...
(OEIS A349635).

Gorovoy, D. and Zmiaikou, D. "On Graphs with Unique Geoodesics and Antipodes." 19 Nov 2021. https://arxiv.org/abs/2111.09987.Sloane,
N. J. A. Sequence A349635 in "The
On-Line Encyclopedia of Integer Sequences."