On The Edge-balance Index Sets Of Nested Graph With The Unlimited Pathes And Equal Pathes And Circles C_n×P_m

The edge-balance index sets of nested graph with the unlimited pathes and equalpathes and circles C_n×P_m is based on the research C_n×P₂and C_n×P₃（n≥3）（reference[38-39]）.With a variety of design skills and the method of classifying, wedivide into three cases, and completely resolve the computational formula and thestructural proof of the edge-balance index sets of C_n×P_m（n≥3, m≥2）.This article firstly complete exact calculation edge of edge-balance index sets nestedgraph with the unlimited pathes and equal pathes and circles.In chapter1, We mainly introduce research status about edge-balance index set ofgraph, and provide some background knowledge and some preliminaries.In chapter2,With6classifications of,we study the edge-balance index sets of×C_n×P_m （n≥3,≡0（mod3））,and determine the formulas and the graphical constructions.In chapter3, We discuss two cases,and finally provide the formula of the edge-balance index sets of C_n×P_m（n≥3, m≡1（mod3））.In chapter4,With4classifications of,We discuss the edge-balance index sets ofC_n×P_m （n≥3, m≡2（mod3））, and complete the formula proof and structural proof.