even vertex

even vertex

[¦ēv·ən ′vər‚teks]
(mathematics)
A vertex whose degree is an even number.
References in periodicals archive ?
Each arc of [[??].sub.k,e] is directed from an even vertex to an odd vertex and each arc of [[??].sub.k, o] is directed from an odd vertex to an even vertex (see Figure 4 for k = 5).
In [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the odd vertices and even vertices alternate and an odd vertex is obtained by adding aj to its preceding (even) vertex, along the anti-directed cycle, and an even vertex is obtained from its preceding (odd) vertex by adding (-bj) to it.
If [x.sub.j] - 2l[b.sub.j], the origin of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], is in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then, as [x.sub.j] - 2l[b.sub.j] is even, it should be of the form [x.sub.j] + r[a.sub.j] - r[b.sub.j], for some r [not equal to] 0 and r [less than or equal to] [2.sup.k-j-1] - 1; r [less than or equal to] [2.sup.k-j-1] - 1 follows from the fact that each anti-directed cycle is of length [2.sup.k-j] and among the vertices of the anti-directed cycle, only half of them can be even vertices and further the origin is an even vertex. Hence [x.sub.j] - 2l[b.sub.j] = [x.sub.j] + r[a.sub.j] - r[b.sub.j] (mod [2.sup.k-1]), that is,
If the number is even, then the vertex is called an even vertex; otherwise it is called an odd vertex.
We will give a construction that gives Type 2 snarks for each even vertex number n [greater than or equal to] 40.
Given such a perfect matching Mo by orienting each of its edges from its odd to its even vertex one gets edges oriented in the directions up, down, left or right.
[M.sub.e](r)) the subset of its edges which are oriented from an odd to an even vertex (resp.