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带弦的圈是协调图
引用本文:徐士达.带弦的圈是协调图[J].应用数学,1995,8(1):31-37.
作者姓名:徐士达
作者单位:江西省上饶师专数学系 334001
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。

关 键 词:    协调标号  协调图  简单图  图论

Cycles with a Chord are Harmonious Graphs
Xu Shida.Cycles with a Chord are Harmonious Graphs[J].Mathematica Applicata,1995,8(1):31-37.
Authors:Xu Shida
Abstract: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.
Keywords:Cycle  Chord  Harmonious labeling
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