联图Cm∨Cn的邻和可区别边染色

doi:10.6040/j.issn.1671-9352.0.2023.385

摘要/Abstract

摘要： 图G的邻和可区别k-边染色是指图G的一个正常边染色中, 满足相邻顶点关联边的色数之和不相等。图G的一个邻和可区别k-边染色所用到的最小颜色数k称为图G的邻和可区别边色数。本文研究了联图C_m∨C_n的邻和可区别边染色问题, 得到了联图C_m∨C_n(n≠m)的邻和可区别边色数及C_n∨C_n的邻和可区别边色数的上界, 并将该结果推广到一般图的联图。

关键词: 圈, 联图, 邻和可区别边染色, 邻和可区别边色数

Abstract: The neighbor sum distinguishing k-edge coloring of graph G is the coloring of a proper edge coloring of graph G, where the chromatic sum of adjacent vertex associated edge are not equal. The minimum number of colors k used for coloring is called the neighbor sum distinguishing edge chromatic numbers of graph G. This paper studies the neighbor sum distinguishing edge coloring problem of the join graph C_m∨C_n, obtaining the neighbor sum distinguishing edgechromatic numbers of the join graph C_m∨C_n(n≠m) and the upper bounds of C_n∨C_n, and extending this result to join graphs of general graphs.

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

中图分类号:

O157

白羽,强会英,何静. 联图C_m∨C_n的邻和可区别边染色[J]. 《山东大学学报(理学版)》, 2025, 60(12): 161-166.

BAI Yu, QIANG Huiying, HE Jing. Neighbor sum distinguishing edge coloring of join graphs C_m∨C_n[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 161-166.

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