摘要
称具有ｅ条边的简单图Ｇ为协调图，若存在由Ｇ的顶点集到模ｅ的整数群Ｚｅ的一个单射ｈ，使得导出映射ｈ＾＊：ｈ＾＊（ｕｖ）≡ｈ（ｕ）＋ｈ（ｖ）（ｍｏｄ ｅ）是一个由Ｇ的边集到Ｚｅ的双射，带弦的圈Ｃ′ｎ是由含ｎ个顶点的圈Ｃｎ上添一条连结两个不相邻顶点的边而得到的图。本文中证明了，除了ｎ＝６且弦端点在Ｃｎ上的距离为２的情况外，所有带弦的圈都是协调图。
A simple graph G with e edges is said a harmonious graph,if there exists an injection h from the vertices set of G to Z,,the group of integers modulo e,so that the induced function h* :k* (uv)=h(u)+A(v)(mod e) is a bijection from the the edges set of G to Z,. A cycle with a chord C'n is obtained from Cn,the cycle with n vertices,by adding one edge joining two nonadjacent vertices.
In this paper ,it's proved that the all cycles with a chord are harmonious graphs except that n = 6 and the distance on Cn between the endpoints of the chord is 2.
出处
《应用数学》
CSCD
北大核心
1995年第1期31-37,共7页
Mathematica Applicata
