# 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.
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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