On Edge-Balance Index Sets of a Nested Graph with Infinite Paths and Power Circles

摘要

We generalize the concept of edge-balanced labeling to the concept of edge-balance index set of graphs. In this article, we define all class of the nested graph with infinite for the integer m ≥ 2, n ≥ 2 and investigate the edge-balance index set of a class graph. In particular, we completely determine the edge-balance index sets of the class graph for the integer m ≥ 3 and solve formula proof and graphic tectonic methods.