ABSTRACT
Graph coloring which has important practical significance and theoretical significance is the main research content. With the wide use of graph coloring in reality, it gradually becomes the important study field for many scholars. Vertex-distinguishing edge coloring or strong edge coloring which is proposed from network problem, biology, information science and computer science is a very difficult problem. In the literature[1-2], vertex-distinguishing edge coloring and adjacent vertex-distinguishing coloring can be studied further. New coloring problems have been proposed constantly, definition of adjacent vertex-distinguishingcoloring, djacent vertexdistinguishing strong and total coloring is proposed in the literature[3-6] related to problems, as well as several kinds of simple graphs related to the coloring chromatic number and some assumptions. This article considers limited simple undirected graph, V (G) and E(G) refers to the graph vertex set and edge set respectively, (G) refers to the maximum degree of graph G. Unspecified graph theory terms and marks used in this article can be referred to in the literature[9].
