### Edge-balanced index sets of five-power-cycle nested graph [(m≡0(mod3))]

ZHENG  Yuge, LIU Jinmeng

1. School of Mathematics and Information Science , Henan Polytechnic University, Jiaozuo, Henan 454003, China
• Online:2015-09-15 Published:2015-10-13

### 5次幂圈嵌套网络图的边-平衡指数集（m模3余0）

1. 河南理工大学 数学与信息科学学院，河南 焦作 454003

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.