mC4的顶点被多重色集合可区别的一般边染色

General Edge-coloring of mC4 which is Vertex Distinguishing by Multisets

简单图G的一个一般边染色是指若干种颜色关于图G的所有边的一个分配,不要求相邻的边被分配不同的颜色.设f是G的使用了k种颜色的一般边染色,若对(?)u,v∈V(G),u≠v,都有与u关联的边的颜色构成的多重集合异于与v关联的边的颜色构成的多重集合,那么称f是使用了k种颜色的顶点被多重色集合可区别的一般边染色.对G进行顶点被多重色集合可区别的一般边染色所需的最少颜色数记为c(G),并且称c(G)为图G的顶点被多重色集合可区别的一般边色数.本文确定了m个C_4的点不交的并mC_4的顶点被多重色集合可区别的一般边色数.

Let G be a simple graph. A general edge-coloring of a graph G is an assignment of a number of colors to the edges. It is not necessary to assign two distinct colors to two adjacent edges. A general edge-coloring f of a graph G is called vertex distinguishing by multisets, if, for any two distinct vertices u, v of a graph G, the multisets of the colors used to color the edges incident with u is different from the multisets of the colors used to color the edges incident with v. The minimum number of colors required for a general edge-coloring of G which is vertex distinguishing by multisets, denoted by c（G）, is called the vertex distinguishing general edge chromatic number of G by multisets. Suppose rnC4 denotes the vertex-disjoint union of m cycles of lengths 4. We will determine c（rnC4） in this paper.