计算机科学 ›› 2015, Vol. 42 ›› Issue (3): 245-251.doi: 10.11896/j.issn.1002-137X.2015.03.051

• 人工智能 • 上一篇    下一篇

两类网络图的边-平衡指数集

刘金萌,侯 涛,郑玉歌   

  1. 河南理工大学数学与信息科学学院 焦作454003,焦作大学机电工程学院 焦作454003,河南理工大学数学与信息科学学院 焦作454003
  • 出版日期:2018-11-14 发布日期:2018-11-14
  • 基金资助:
    本文受国家自然科学基金项目(51175153 /E050903)资助

On Edge-balanced Index Sets of Two Classes of Nested Network Graph

LIU Jin-meng, HOU Tao and ZHENG Yu-ge   

  • Online:2018-11-14 Published:2018-11-14

摘要: 在较小次幂圈嵌套网络图的基础上,研究了10次幂嵌套网络图的边-平衡指数集。利用基础图、带齿套圈子图、单点扇形子图设计新思路,降低了构造标号图的复杂程度。当n=10为偶数时,提出了新的变换指数方法,简化了证明过程。确定了m模6余1和余3且m大于等于2时(m为圈数)无限路10次幂圈嵌套图的边-平衡指数集,并且解决了这两类幂圈嵌套图的边-平衡指数集的存在性,给出了具体构造方法和公式证明。

关键词: 边-友好标号,边-平衡指数集,10次幂圈嵌套图,带齿套圈子图,单点扇形子图

Abstract: On the basis of smaller power-cycle nested network graph,the edge-balanced index sets of ten-power-cycle nested network graph were investigated.It reduces the difficulty of ten-power-cycle nested network graph labeling using the novel design of the basic graph,nested-cycle subgraph with gear and single-point sector subgraph.When n is an even number,a new method of changing index was provided,simplifying the proving process.The edge-balanced index sets of ten-power-cycle nested graph were determined when m≡1,3(mod 6) and m≥2.This paper proved the existence of the edge-balanced index sets of two classes of nested network graph.The computational formulas and the construction of the corresponding graphs were also provided.

Key words: Edge-friendly labeling,Edge-balanced index set,Ten-power-cycle nested graph,Nested-cycle subgraph with gear,Single-point sector subgraph

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