The Sigma Chromatic Number Of Some Graphs

Graph coloring and chromatic number problem are important research contents of Graph Theory. They are among the most active areas of people’s research, and have rich theoretical results and practical applications. The reference theory and method occupy an important position in discrete mathematics. Graph vertex coloring is a hot issue of coloring. Many scholars use different methods to color vertex, and have received many excellent results. In 2002 year, the United States Western Michigan University Chartrand proposed sigma coloring concepts. This is a new class of vertex coloring. In this paper, some special classes of graphs sigma coloring are studied. The main work done in this paper includes:(1) It proposes windmill, kind of windmills Dm,n,wheel graph of sigma coloring scheme, and calculates the number of sigma chromatic number, and proves their sigma continuous.(2) It proposes square mesh graph and the honeycomb mesh graph of sigma coloring scheme in plane rules, and calculates the number of sigma chromatic number, and proves their sigma continuous.(3) Based on breadth first and recursion algorithm,it proposes the tree sigma coloring algorithm, and proves the validity of the algorithm.