单圈图的D(2)-点和可区别边染色  

D(2)-Vertex Sum Distinguishing Edge Coloring of Unicyclic Graphs

作　　者：刘欢 强会英[1] 王洪申[2] Liu Huan;Qiang Huiying;Wang Hongshen(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：《南开大学学报（自然科学版）》2024年第1期91-97,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(61962035)。

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.Let ϕ be 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 ■,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 

分 类 号：O157.5[理学—数学]