摘要
图G的D(2)-点和可区别全染色是指在图G的一个正常全染色φ下,G中任意两个距离不超过2的顶点u,v,其色集合中所有颜色数之和互不相同.使得G有一个k-D(2)-点和可区别全染色的最小整数k,称为图G的D(2)-点和可区别全色数.文中应用组合零点定理和权转移方法刻画了单圈图的D(2)-点和可区别全染色,并得到其D(2)-点和可区别全色数.
Letφbe a proper total coloring of graph G,for any u,v∈V(G),if d_(G)(u,v)≤2 such that g(u)≠g(v),where g(u)=φ(u)+∑_(uωϵE(G))φ(uω),thenφis the 2-distance sum distinguishing total coloring of graph G.The D(2)-vertex sum distinguishing total chromatic numbersχ_(2)′′-Σ(G)of graph G is the smallest integer k such that the graph G has a D(2)-vertex sum distinguishing total coloring.This paper fully characterizes the D(2)-vertex sum distinguishing total coloring of unicyclic graphs by using combinatorial nullstellsatz and discharging method,and obtain their the D(2)-vertex sum distinguishing total chromatic numbers.
作者
强会英
刘欢
王洪申
QIANG Hui-ying;LIU Huan;WANG Hong-shen(School of Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China;College of Mechanical and Electrical Engineering,Lanzhou University of Technology,Lanzhou 730050,China)
出处
《高校应用数学学报（A辑）》
北大核心
2024年第3期371-378,共8页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11961040)。
关键词
单圈图
全染色
D(2)-点和可区别全染色
权转移方法
unicyclic graph
total-coloring
D(2)-vertex sum distinguishing total coloring
dis-charging method
