两类网络图的边-平衡指数集

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

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。

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 nis 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.