完全二部图K_(11,n)(11≤n≤88)的点可区别E-全染色  

Vertex-distinguishing E-total coloring of a complete bipartite diagram K_(11,n)(11≤n≤88)

作　　者：汉大玮 陈祥恩 HAN Da-wei;CHEN Xiang-en(School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《广州大学学报（自然科学版）》2022年第1期10-17,共8页Journal of Guangzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11761064,61163037)。

摘　　要：设图G是简单图,如果给图G中相邻的2个顶点染有不同的颜色,并且让这2个顶点的每条关联边和关联边的端点染不相同颜色的一个全染色称为图G的一个全染色f。如果满足条件对■u,v∈V(G),u≠v,存在C(u)≠C(v),那么f叫做图G的一个E-全染色,简称为VDET染色。文章利用反证法和分析法,讨论完全二部图K11,n(11≤n≤88)的点可区别E-全染色问题,并利用构造染色法,给出完全二部图K11,n(11≤n≤88)的最优点可区别E-全染色染色方案。Let us say G is a simple graph.The coloring f of diagram G is called an E-total complete coloring if two adjacent top points in graph G are dyed different colors,and dot each associated edge a different color from its end.For an E-complete stain coloring of graph G,if C(u)≠C(v)for any two different vertices u and v of V(G),we shall abbreviate the“VDET”.By using analytical method and proof by contradiction,this paper discusses the vertex-distinguishing E-total(VDET)coloring problem of a complete bipartite graph K11,n(11≤n≤88),and the structure staining method was used to give the best staining scheme of optimal VDET coloring of a complete bipartite graph K_(11,n)(11≤n≤88).

关 键 词：E-全染色 VDET染色 VDET染色色数 完全二部图 

分 类 号：O157.5[理学—数学]