K_(5,5,p)的点可区别的IE-全染色(p≥2028)  

Vertex-distinguishing IE-total coloring of K_(5,5,p)(p≥2028)

作　　者：闫瑞敏 陈祥恩 YAN Ruimin;CHEN Xiang’en(College 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,兰州730070

出　　处：《华东师范大学学报（自然科学版）》2022年第2期16-23,共8页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11761064,61163037)。

摘　　要：图G的IE-全染色f是指对■u,u∈V(G),使得f(u)≠f(v)的一个一般全染色,其中u,v相邻,V(G)是图G的顶点集,设f是图G的IE-全染色,图G的一个顶点x在f下的色集合C(x)是指由x及x的关联边的颜色所构成的集合(非多重集).若图G的任意两个不同顶点的色集合不同,则f称为图G的点可区别的IE-全染色(简记为VDIETC).利用色集合事先分配法、构造染色法及反证法探讨了完全三部图K_(5,5,p)(p≥2028)的点可区别的IE-全染色问题,确定了K_(5,5.p)(p≥2028)的点可区别的IE-全色数.Let G be a simple graph.A total coloring f of G is called an IE-total coloring if f(u)≠f(v)for any two adjacent vertices u and v,where V(G)denotes the set of vertices of G.For an IE-total coloring f of G,the set of colors C(x)(non-multiple sets)of vertex x under f of G is the set of colors of vertex x and of the edges incident with x.If any two distinct vertices of G have distinct color sets,then f is called a vertex-distinguishing IE-total coloring of G.We explore the vertex distinguishing IE-total coloring of complete tripartite graphs K_(5,5,p)(p≥2028)through the use of multiple methods,including distributing the color sets in advance,constructing the colorings,and contradiction.The vertex-distinguishing IE-total chromatic number of K_(5,5,p)(p≥2028)is determined.

关 键 词：完全三部图 IE-全染色 点可区别的IE-全染色 点可区别的IE-全色数 

分 类 号：O157.5[理学—数学]