完全二部图K_(12,n)(12≤n≤88)的点可区别E-全染色  

Vertex-distinguishing E-total coloring of complete bipartite graph K_(12,n) for 12≤n≤88

作　　者：胡开洋 黄明芳[1] 马宝林 HU Kaiyang;HUANG Mingfang;MA Baolin(School of Science,Wuhan University of Technology,Wuhan 430070,Hubei,China;School of Mathematics and Science,Henan Institute of Science and Technology,Xinxiang 453003,Henan,China)

机构地区：[1]武汉理工大学理学院,湖北武汉430070 [2]河南科技学院数学科学学院,河南新乡453003

出　　处：《山东大学学报（理学版）》2024年第6期36-43,70,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12261094)。

摘　　要：图G的一个E-全染色是指图G中存在一个映射f:V∪E→{1,2,…,k},对于任意边e=uv∈E(G),有f(e)≠f(u),f(e)≠f(v)且f(u)≠f(v)。在E-全染色f下,令C(v)表示顶点v所染的颜色及与顶点v相邻的边所染的颜色所构成的集合。若∀u,v∈V(G),u≠v有C(u)≠C(v),则称f为图G的k-点可区别E-全染色,简称k-VDET染色。本文证明了完全二部图K12,n分别在12≤n≤28下的6-VDET染色和29≤n≤88下的7-VDET染色。An E-total coloring of graph G is a mapping f:V∪E→{1,2,…,k}such that for each edge e=uv∈E(G),f(e)≠f(u),f(e)≠f(v)and f(u)≠f(v).For an E-total coloring f of a graph G,let C(v)denote the set of colors of vertex v and the edges incident with v.If C(u)≠C(v)where u,v∈V(G)and u≠v,then that f is a k-vertex-distinguishing E-total coloring of graph G,or simply k-VDET coloring.This paper proves 6-VDET coloring and 7-VDET coloring of complete bipartite graph K12,n for 12≤n≤28 and 29≤n≤88,respectively.

关 键 词：完全二部图 E-全染色 点可区别E-全染色 

分 类 号：O157.5[理学—数学]