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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (9): 29-35.doi: 10.6040/j.issn.1671-9352.0.2018.144

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路的联的邻和可区别边染色

田双亮1,2,杨环1,杨青1,索郎王青1   

  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

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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(x)表示顶点x关联边的颜色之和,即wσ(x)=∑e??綍xσ(e),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χ'∑(G)。 本文给出了两条不同阶路的联的邻和可区别边色数的精确值。另外, 得到了同阶路的邻和可区别边色数的上界。

关键词: 路, 联, 邻和可区别边染色, 邻和可区别边色数

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.

Key words: path, join, neighbor sum distinguishing edge coloring, neighbor sum distinguishing edge chromatic number

中图分类号: 

  • O157.5
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