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中文摘要：
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颜色的最少数目记为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。讨论了m个Pn的点不交的并m Pn的顶点被多重色集合可区别的一般边色数。
英文摘要：
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 distinguished by multisets,if,for any two distinct vertices u,v of a graph G,the multiset of the colors used to color the edges incident with u is different from the multiset 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 m Pn denotes the vertex-disjoint union of m paths of length n. The vertex distinguishing general edge-coloring（ by multisets）of m Pnwill be discussed.
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