The Vertex-Adjacent Vertex Distinguishing Total Coloring Of Some Graphs

Graph coloring is one of the main contents of graph theory.In recent years,more and more people start to study graph coloring, some important results are obtained and many new coloring concepts are brought up. In this paper, new coloring problems of some graphs are studied. The paper has six parts:In the first part, the related concepts, terminologies and symbols are introduced. In the second part,the vertex-adjacent vertex distinguishing total coloring of join graphs are discussed. In the third part,the vertex-adjacent vertex distinguishing total coloring of some product graphs is discussed. In the fourth part,the vertex-adjacent vertex distinguishing total coloring of some double graphs are discussed. In the fifth part,the vertex-adjacent vertex distinguishing total coloring of some general Mycielski graphs are discussed. In the sixth part,the probability estimates of vertex-adjacent vertex distinguishing total chromatic number of some graphs are discussed.