5次幂圈嵌套网络图的边-平衡指数集(m模3余0)

Edge-balanced index sets of five-power-cycle nested graph(m≡0(mod 3))

针对网络图边-平衡指数集标号问题,在等圈嵌套网络图的基础上,提出了幂圈嵌套网络图的概念,进而研究5次幂圈嵌套网络图的边-平衡指数集。利用基础图、带齿套圈子图、五点扇形子图组设计新思路,大大降低了构造标号图的复杂程度,确定了当m≡0(mod 3)且m≥4时,5次幂圈嵌套网络图的边-平衡指数集,并且给出了边-平衡指数集对应图形标号的设计方法。

To cope with the edge-balanced index sets of network graph labeling, on the basis of the equal-cycle nested network graph, a new concept of power-cycle nested network graph is proposed. Moreover, the edge-balanced index sets of five-power-cycle nested network graph are investigated. It reduces the difficulty of five-power-cycle nested network graph labeling because of the novel design of the basic graph, nested-cycle subgraph with gear and five-vertex sector subgraph group. The results show the edge-balanced index sets of five-power-cycle nested network graph when m≡0（mod 3） and m≥4. At the same time, the design methods of the corresponding graphs are also provided.