On The Edge-Balance Index Sets Of C_n×P_m

The edge-balance index set of graph, an important issue to research in GraphTheory, is the matching of vertex and edge of graph with Z₂ through the mappingfunction, and further studies the characteristics and inherent properties of those graphs,which can be applied to information engineering, communication networks, computerscience, economic management, and medicine, etc. This paper aims to do some pioneerresearch of the nested graph.We use the important method of classifying n and resolve the computational formulaand the constructor to research the edge-balance index sets of C_n×P_m(n≥3,m = 2,3).In chapter 1, we introduce some preliminaries about Boolean index set of graphand provide some background knowledge and prior research.In chapter 2, according to the definition of edge-friendly and the relation of theedge, we work out the exact classification of n with a large number of graphic structure.When m = 2, the all edge-balance index sets of C_n×P₂ are analyzed and determinedby studying the maximum edge-balance index of the classification 4 of n.In chapter 3, when n = 3, with 6 classifications of n and the graphic structure, westudy the maximum edge-balance index of n≡0,1(mod6), determine the edge-balanceindex sets of C_n×P₃, and give the formula proof and structure graphs.In chapter 4, we research the edge-balance index sets of C_n×P₃ when n≡2,3(mod6),and give the formula proof and structure graphs.Finally, we research the edge-balance index sets of C_n×P₃ when n≡4,5(mod6),and give the formula proof and structure graphs.