On Some Coloring Of Graph

Graph coloring is a very difficult problem in graphs theory. It attracts many researchers to work at it. They have obtained a lot of results on normal edge coloring. There are some other conoptions based on different problems in fact, such as the number of storehouses, map colorings which induces edge coloring, wire network and wireless network inworking adjacent vertex distinguishing edge coloring, which attract many researchers who have gained many conclusions. The total coloring is based on the vertex coloring and edge coloring, there are series of papers and works on it. Recently, the vertex-distinguishing total coloring is research fewly for its difficult.The edge coloring problems contain proper edge coloring, adjacent vertex-distinguishing edge coloring, vertex-distinguishing, and so on.In this paper, we discuss six edge coloring problems, such as proper edge coloring, adjacent vertex distinguishing edge coloring, vertex distinguishing edge coloring, interval edge coloring, interval vertex total coloring and perfect total coloring. For different graphs, we use different coloring methods to prove it. The interval edge coloring, interval vertex total coloring and perfect total coloring is due to me. In this paper, we present some new conjectures which is advanced.