# opposite vertices

## opposite vertices

[′äp·ə·zət ′vərd·ə‚sēz]
(mathematics)
Two vertices of a polygon with an even number of sides that have the same number of sides between them along either path around the polygon from one vertex to the other.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Then G has two M-alternating Hamiltonian paths each starting at [w.sub.1] and ending at diametrically opposite vertices of the last canonical 4-cycle.
Proposition 2 (a) If d [greater than or equal to] 3 is odd, and v, v' are diametrically opposite vertices of [Q.sub.d], then [Q.sub.d] - v - v' has a Hamiltonian cycle.
(b) If d [greater than or equal to] 4 is even, and v, u are neighbors, and v, v' are diametrically opposite vertices of [Q.sub.d], and u, u' are diametrically opposite vertices of [Q.sub.d], then [Q.sub.d] - v - v' - u - u' has a Hamiltonian cycle.
Converse follows from the fact that if M = V(G), then the distance patterns of diametrically opposite vertices are identical.
Here a cube has been created, and a polygon AJGL formed using two opposite vertices and two midpoints of edges.
An s-domino contains two pairs of opposite vertices.
Lemma 8 Every 4-total-coloring [C.sup.T] of an s-domino is such that, for one pair of opposite vertices x and y, the following holds: [C.sup.T] (x) = [C.sup.T] (y) and [C.sup.T] (x*) = [C.sup.T] (y*).

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