%0 Journal Article
%T 完全二部图K10,n(10≤n≤90)的点可区别E-全染色<br>Vertex-distinguishing E-total coloring of complete bipartite graph K10,n with 10≤n≤90
%A 包丽娅
%A 陈祥恩
%A 王治文
%J 山东大学学报（理学版）
%D 2018
%R 10.6040/j.issn.1671-9352.0.2018.605
%X 摘要： 图G的一个E-全染色f是指使相邻点染以不同颜色且每条关联边与它的端点染以不同颜色的全染色。对图G的一个E-全染色f,一旦∠u,v∈V(G), u≠v,就有C(u)≠C(v),其中C(x)表示在f下点x的颜色以及与x关联的边的色所构成的集合,则f称为图G的点可区别的E-全染色,简称为VDET染色。令χevt(G)=min{k|G存在k-VDET染色},称χevt(G)为图G的点可区别E-全色数。利用分析法和反证法,讨论并给出了完全二部图K10,n(10≤n≤90)的点可区别E-全色数。<br>Abstract: Let G be a simple graph. An E-total coloring f of G is called that if there are no two adjacent vertices of G receive the same color, and no edges of G receives the same color as one of its endpoints. For an E-total coloring f of G, if C(u)≠C(v) for any two distinct vertices u and v of V(G), where C(x) denotes the set of colors of vertex x and of the edges incident with x under f, then f is called a vertex-distinguishing E-total coloring of G. Let χevt(G)=min{k|G has a k-VDET coloring}. Then χevt(G) is called the VDET chromatic number of G. By using analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K10,n is discussed and the VDET chromatic number of K10,n(10≤n≤90) has been obtained
%K 完全二部图
%K E-全染色
%K 点可区别E-全染色
%K 点可区别E-全色数
%K &lt
%K br&gt
%K complete bipartite graphs
%K E-total coloring
%K vertex-distinguishing E-total coloring
%K vertex-distinguishing E-total chromatic number
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2018.605