Abstract: 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(mod3)] and [m4]. At the same time, the design methods of the corresponding graphs are also provided.

Key words: edge-friendly labeling, edge-balanced index set, five-power-cycle nested graph, nested-cycle subgraph with gear, five-vertex sector subgraph group

摘要： 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(mod3)]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。

关键词: 边-友好标号, 边-平衡指数集, 5次幂圈嵌套图, 带齿套圈子图, 五点扇形子图组