《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (9): 29-35.

• •

### 路的联的邻和可区别边染色

1. 1.西北民族大学数学与计算机科学学院, 甘肃 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, 甘肃 兰州 730030
• 发布日期:2020-09-17
• 作者简介:田双亮(1965— ), 男, 硕士, 教授, 研究方向为图论及组合优化. E-mail:sl_tian@163.com
• 基金资助:
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(14XBZ018)

### Neighbor sum distinguishing edge coloring of the join of paths

TIAN Shuang-liang1,2, YANG Huan1, YANG Qing1, SUOLANG Wang-qing1

1. 1. School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China;
2. Key Laboratory of Streaming Data Computing Technologies and Applications, Northwest Minzu University, Lanzhou 730030, Gansu, China
• Published:2020-09-17

Abstract: A proper ［k］-edge coloring σ of a graph G is a k-proper-edge-coloring of G using colors in ［k］={1,2,…,k}, let wσ(x)denote the sum of the colors of edges incident with x, i.e., wσ(x)=∑e??綍xσ(e), and wσ(x)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 weight. 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 χ'(G). The exact values of the neighbor sum distinguishing edge chromatic number of the join of two paths with different orders are given. The upper bound of the neighbor sum distinguishing edge chromatic number of the join of two paths with same orders is obtained.

• O157.5
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