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Antipode


Given a point P, the point P^' which is the antipodal point of P is said to be the antipode of P.

The term antipode is also used in plane geometry. Given a central conic (or circle) and a point P lying on it, draw a line passing through P and the center O of the conic. Then the antipode P^' of P is other point lying on the conic through which the line PO passes.

The antipode of a vertex v_i in a graph is a vertex v_j at greatest possible distance from v_i. An antipodal graph is then defined as a connected graph in which each vertex has exactly one antipode (Gorovoy and Zmiaikou 2021).


See also

Antipodal Graph, Antipodal Points

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References

Gorovoy, D. and Zmiaikou, D. "On Graphs with Unique Geoodesics and Antipodes." 19 Nov 2021. https://arxiv.org/abs/2111.09987.Tietze, H. Famous Problems of Mathematics: Solved and Unsolved Mathematics Problems from Antiquity to Modern Times. New York: Graylock Press, p. 25, 1965.

Referenced on Wolfram|Alpha

Antipode

Cite this as:

Weisstein, Eric W. "Antipode." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Antipode.html

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