【摘要】 图G的正常[k]-边染色σ是指颜色集合为[k]={1,2,...,k}的G的一个正常边染色.用w_σ(χ)表示顶点χ关联边的颜色之和,即■,并称w_σ(x)为x关于σ的权.图G的k-邻和可区别边染色是指相邻顶点具有不同权的正常[k]-边染色,最小的k值称为G的邻和可区别边色数,记为x′_Σ(G).现得到了路P_n与简单连通图H的字典积P_n[H]的邻和可区别边色数的精确值,其中H分别为正则第一类图、路、完全图的补图.更多还原

【Abstract】 A proper [k]-edge coloring σ of graph G is a k-proper-edge-coloring of graph G using colors in [k]={1,2,…,k}.Let W_σ(χ) denote the sum of the colors of edges incident with x,i.e.■,and w_σ(χ) is called the weight of the vertex x with respect to σ.A neighbor sum distinguishing edge coloring σ of G is a proper[k]-edge coloring of G such that no pair adjacent vertices receive the same weights.The smallest value k for which G has such a coloring is called the neighbor sum distinguishing edge chromatic number of G and denoted by We obtained the exact values of this parameter for the lexicographic product P [H] of a path P_n and a connected simple graph H,where is a Class 1 regular graph,a path,the complement of a complete graph,respectively.更多还原