The Fractional Chromtic Numbers And Total Fractional Chromtic Numbers Of Some Graphs

The issue of coloring is a very important problem in the graph theory. The fractional chromatic number of a graph is a variation of the chromatic number. It can provide a better model for some special problems. As an important parameter, the chromatic number of the graph has the values of study.In the second chapter, the equivalent definition of fractional chromatic number is given, then we mostly study the fractional chromatic number of some special graphs, including the Star Graph, Windmill Graph, Crown Graph and Gear Graph.In the third chapter, we firstly study the definition of circulant graph and adjacency matrix. Then, we show the fractional chromatic number of two classes of 6-regular circulant graphs by constructing the largest independent set and fractional coloring of a graph G.In the fourth chapter, the equivalent definition of general Peterson Graph is given, and we mostly study the fractional chromatic number of general Peterson Graph when k is equal to 3.In the fifth chapter, according to the conjecture of total coloring, the total fractional chromatic number of some Mycielski Graph is studied, including Star Graph, Fan Graph, Wheel Graph and Crown Graph Gn,2·It exploits the area of the graph coloring and makes for studying the structure of graphs.