路的字典积的邻和可区别边染色  

Neighbor sum distinguishing edge coloring of the lexicographic product of paths

作　　者：田双亮[1,2] 杨环 索郎王青 杨青 TIAN Shuangliang;YANG Huan;SUOLANG Wangqing;YANG Qing(School of Mathematics and Computer Science,Northwest Minzu University,Lanzhou 730030,China;Key Laboratory of Streaming Data Computing Technologies and Applications,Northwest Minzu University,Lanzhou 730030,China)

机构地区：[1]西北民族大学数学与计算机科学学院,兰州730030 [2]西北民族大学动态流数据计算与应用重点实验室,兰州730030

出　　处：《运筹学学报》2020年第1期140-146,共7页Operations Research Transactions

基　　金：西北民族大学科研创新团队计划资助;国家民委科研资助项目(No.14XBZ018)

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wσ(χ)表示顶点χ关联边的颜色之和,即■,并称wσ(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Pn与简单连通图H的字典积Pn[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.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 Wσ(χ) denote the sum of the colors of edges incident with x,i.e.■,and wσ(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.

关 键 词：路 字典积 邻和可区别边染色 邻和可区别边色数 

分 类 号：O157.5[理学—数学]