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Based on the research of Power-cycle Nested Graph , the decomposition method of single point sector has come up. By the use of the process of clawed nested-cycle sub-graph, the edge-balanced index sets of the power-cycle nested graph  are solved when and  . Besides, the constructive proofs of the computational formulas are also completed. The theory can be applied to information engineering, communication networks, computer science, economic management, medicine, etc. The proving method can be a reference to solve the problem of the power-cycle nested graph

On the Edge-balanced Index Set of a class of Power-cycle Nested Network Graph