单圈图的D(2)-点和可区别边染色
D(2)-Vertex Sum Distinguishing Edge Coloring of Unicyclic Graphs
刘欢 1强会英 1王洪申2
作者信息
- 1. 兰州交通大学数理学院,甘肃兰州 730070
- 2. 兰州理工大学机电工程学院,甘肃兰州 730050
- 折叠
摘要
图G的D(2)-点和可区别边染色是指在图G的一个正常边染色φ下,G中任意的两个距离不超过2的顶点u,v,其关联边的色数和互不相等.使得G有一个D(2)-点和可区别边染色的最小整数k称为图G的D(2)-点和可区别边色数.完整刻画了单圈图的D(2)-点和可区别边染色,并得到了其D(2)-点和可区别边色数.
Abstract
Letφbe a proper edge coloring of graph G,for any u,v∈V(G),if dG(u,v)≤ 2 such that S(u)≠S(v),where S(u)=Σuw∈E(G)φ(uw),then φ is the 2-distance sum distinguishing edge coloring of graph G.The D(2)-vertex sum distinguishing edge chromatic numbers of graph G is the smallest integer k such that the graph G has a D(2)-vertex sum distinguishing edge coloring.The D(2)-vertex sum distinguishing edge coloring of unicyclic graphs are fully characterized and their the D(2)-vertex sum distinguishing edge chromatic numbers are obtained.
关键词
单圈图/边染色/D(2)-点和可区别边染色/D(2)-点和可区别边色数Key words
unicyclic graph/edge-coloring/D(2)-vertex sum distinguishing edge coloring/D(2)-vertex sum distinguishing edge chromatic number引用本文复制引用
出版年
2024
NETL
NSTL
万方数据