无限路等圈嵌套图边-平衡指数集的完全确定（1）

上海交通大学学报（自然版） ›› 2013, Vol. 47 ›› Issue (07): 1160-1163.

无限路等圈嵌套图边-平衡指数集的完全确定（1）

郑玉歌1，姚景景2

（1．河南理工大学数学与信息科学学院，河南焦作 454003； 2．六盘水师范学院数学系，贵明六盘水 553004）

收稿日期:2012-04-16 出版日期:2013-07-30 发布日期:2013-07-30
基金资助:
河南省教育厅科学技术研究重点项目资助（12B110009），河南省应用数学重点学科资助.河南省运筹学与控制论重点学科资助.

Edge-balance Index Sets of Nested Graph with Unlimited Paths and Equal Circles（1）

ZHENG Yuge1,YAO Jingjing2

(1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, Henan, China; 2. Department of Mathematics, Liupanshui Normal University, Liupanshui 553004, Guizhou, China)

Received:2012-04-16 Online:2013-07-30 Published:2013-07-30

摘要/Abstract

摘要：

基于Cn×P3，Cn×P11图的边-平衡指数集,利用多种组合设计技巧,找出对一切自然数m和n的有效分类,研究了无限路等圈嵌套图Cn×Pm的边-平衡指数集问题,确定了n≥3,m≡0(mod3)时，Cn×Pm的边-平衡指数集的计算公式及相应的图形设计方法.

关键词: 边-友好指数集, 边-平衡指数集, 图Cn×, Pm

Abstract:

Based on the study of the edge-balance index sets of Cn×P3，Cn×P11, this paper introduced several novel techniques of combinatorial design which generalized the effective classification of all natural numbers m and n. These ideas help to examine the problem of the edge-balance index sets of the nested graph Cn×Pm with unlimited paths and equal circles，obtaining the computational formula of the edge-balance index sets Cn×Pm(n≥3,m≡0(mod3)), and presenting the way to design the graphs.

Key words: edge-friendly labeling, edge-balance index, graph Cn×Pm

中图分类号:

O 157.5

郑玉歌1，姚景景2. 无限路等圈嵌套图边-平衡指数集的完全确定（1）[J]. 上海交通大学学报（自然版）, 2013, 47(07): 1160-1163.

ZHENG Yuge1,YAO Jingjing2. Edge-balance Index Sets of Nested Graph with Unlimited Paths and Equal Circles（1）[J]. Journal of Shanghai Jiaotong University, 2013, 47(07): 1160-1163.

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