Study On The Adjacent Vertex-distinguishing Total Coloring Of Graphs

Graph coloring theory as an important research topic in the Graph Theory, has been greatly loved by researchers, and so far, have had rich research results. The earliest Research topics are the classical Coloring Problems like the point Coloring Problem and the edge Coloring Problem and then the Coloring Problem gained expanded on the basis of classical Coloring Problems. In 2004 ,Zhang Zhong-fu proposed the concept of Adjacent Vertex Distinguishing Total Coloring and gained the concept of Adjacent Vertex Distinguishing Total Coloring of path,cycle,complete cycle,complete bipartite graphs,stars, fans and wheels,and gained corresponding Adjacent Vertex Distinguishing Total Coloring of path And gained the suppose: For the connected graph whose order are not less than 2 have the conclusion:χat(G)≤Δ(G)+3In 2006, Li Guang-hai, Li Wu-zhuang study the gear graph in the paper on several types of Adjacent vertex distinguishing total coloring. In this paper,we gained four new gear graph by add the edges on the basis of original gear graph and gained the corresponding adjacent vertex-distinguishing total chromatic number. The main findings are as follows:...