无K4-子式图的2-距离和可区别边染色

doi:10.6040/j.issn.1671-9352.0.2020.198

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (11): 83-86.doi: 10.6040/j.issn.1671-9352.0.2020.198

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无K₄-子式图的2-距离和可区别边染色

强会英,姚丽^*

兰州交通大学数理学院, 甘肃兰州 730070

发布日期:2021-11-15
作者简介:强会英(1968— ),女,硕士,教授,研究方向为图论及其应用. E-mail:qhy2005ww@126.com*通信作者简介:姚丽(1995— ),女,硕士,研究方向为图论及其应用. E-mail:YaoL08@163.com
基金资助:
国家自然科学基金资助项目(61962035)

2-distance sum distinguishing edge coloring of K₄-minor-free graphs

QIANG Hui-ying, YAO Li^*

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Published:2021-11-15

摘要/Abstract

摘要： 图G的一个正常边染色φ若满足:∠u,v∈V(G),且d_G(u,v)≤2都有f(u)≠f(v),其中f(u)=∑_uw∈E(G)φ(uw),则称φ为图G的2-距离和可区别边染色。运用反证法,结合构造染色函数法,研究了无K₄-子式图的2-距离和可区别边染色,确定了无K₄-子式图的2-距离和可区别边色数的一个上界。

关键词: 2-距离和可区别边染色, 2-距离和可区别边色数, 无K₄-子式图

Abstract: Let φ be a proper edge coloring of graph G, for any u,v∈V(G), if d_G(u,v)≤2 such that f(u)≠f(v) where f(u)=∑_uw∈E(G)φ(uw), then φ is the 2-distance sum distinguishing edge coloring of graph G. The 2-distance sum distinguishing edge coloring of K₄-minor-free graphs are studied by using the methods of contradiction and constructing coloring function, and a upper bound of the 2-distance sum distinguishing edge chromatic number of K₄-minor-free graphs is obtained.

Key words: 2-distance sum distinguishing edge coloring, 2-distance sum distinguishing edge chromatic, K₄-minor-free graphs

中图分类号:

O157.5

强会英,姚丽. 无K₄-子式图的2-距离和可区别边染色[J]. 《山东大学学报(理学版)》, 2021, 56(11): 83-86.

QIANG Hui-ying, YAO Li. 2-distance sum distinguishing edge coloring of K₄-minor-free graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 83-86.

参考文献

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无K₄-子式图的2-距离和可区别边染色

2-distance sum distinguishing edge coloring of K₄-minor-free graphs

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