Research On General Edge-coloring Of Several Classes Of Graphs Which Are Vertex Distinguishing By Multisets

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. In the paper, general edge-coloring of m C₄, m C₆ and m P_n which are vertex distinguishing by multisets are discussed by the method of constructing coloring, the vertex distinguishing by multisets general edge chromatic number of m C₄, m C₆ and m P_n are obtained.