若干图的集合点染色  

On the Set-vertex Colouring of Some Graphs

作　　者：王鸿杰[1] 李沐春[1] 贾泽乐 WANG Hong-jie;LI Mu-chun;JIA Ze-le(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《兰州交通大学学报》2020年第4期126-131,共6页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(11961041,61163010);兰州交通大学青年基金(2016014,2017004,2017021)。

摘　　要：图G的集合点染色是集合X中的非空子集在点集V(G)上的一个分配,满足相邻点的色集合不相同、相邻点上色集合交不为空集,且每个点上的色集合长度不低于该点的度.此时把X中包含颜色的最小数目称为图G的集合点色数.应用构造染色函数法和色集合分配法研究圈、路、轮、扇、星以及路与路的联图,得到确切的集合点色数,进一步推出圈与圈的联图、路与圈的联图的集合点色数.The set-vertex coloring of graph G is an assignment of the non-empty subsets of X on vertex set V(G),which satisfies that the cardinal number of color set on each vertex is no less than its degree,the intersection of the color sets of adjacent points is not an empty set,and the intersection of color sets on adjacent vertices is not empty.Then the minimum number of colors contained in X is called set-vertex chromatic number of graph G.The methods of constructing coloring function and color set assignment are applied to study the joint graphs of circles,path,wheels,fans,stars and obtain the exact set-vertex chromatic numbers.Furthermore,the set vertex chromatic number of joint graphs of loop and loop,the path and loop are deduced.

关 键 词：联图 集合点染色 集合点色数 

分 类 号：O157.5[理学—数学]