单圈图的D(2)-点和可区别全染色  

D(2)-vertex sum distinguishing total coloring of unicyclic graphs

作　　者：强会英[1] 刘欢 王洪申[2] 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)

机构地区：[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

出　　处：《高校应用数学学报（A辑）》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)。

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.

关 键 词：单圈图 全染色 D(2)-点和可区别全染色 权转移方法 

分 类 号：O157.5[理学—数学]