完全二部图K_11,n(89≤n≤212)的点可区别E-全染色

Vertex-Distinguishing E-Total Coloring of Complete Bipartite Graph K_11,n(89≤n≤212)

摘要: 图G的一个E-全染色f是指让相邻两个顶点之间染不同的颜色，并且让每条关联边与它的端点染不同颜色的全染色。如果对图G中任意两个不同的顶点u和v，点u和点v的色集合不相同，则称f为图G的VDET染色，即图G的点可区别E-全染色。在本篇论文中我们利用反证法以及分析法，讨论完全二部图K_11,n(89≤n≤212)的VDET染色问题，并利用构造染色法给出K_11,n(89≤n≤212)的最优VDET染色的染色方案。

Abstract: Let G be a simple graph. The total coloring f of G is called an E-total coloring if two adjacent vertices have different colors, and dot each associated edge a different color from its end. For an VDET coloring f of graph G, if C（u）≠C（v） for any two distinct vertices u and v of V(G), then f is called VDET; we shall abbreviate the vertex-distinguishing E-total coloring of G. This paper uses the contradiction and analysis method. We discussed the VDET coloring problem of complete bipartite graph K_11,n(89≤n≤212). The structure staining method was used to give the best staining scheme of optimal VDET coloring of complete bipartite graph K_11,n(89≤n≤212).