JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (9): 29-35.doi: 10.6040/j.issn.1671-9352.0.2018.144

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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.

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

CLC Number: 

  • O157.5
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