The Study On R-hued Coloring And Square Coloring Of Several Types Of Graphs

Graph coloring problem is one of the most important problems in the study of graph theory, has great theoretical significance and practical value. First originated in the map of the "Four Color Conjecture", studied the coloring problem. After more than a century of research, based on the classical vertex coloring and edge coloring, produce many new coloring. For example:star coloring, cyclic coloring, total coloring, distance coloring, acyclic coloring, incidence coloring, fractional coloring, r-hued coloring and linear coloring. In recent years, coloring of graphs is very active. The r-hued coloring is proposed in recent years. Lai Hongjian is propose r-hued coloring in 2006. Square coloring is one kind of special label coloring. Label coloring appeared in the ninety’s of the last century, it is a kind of special vertex coloring of Graphs. In recent years, through the research of square coloring and r-hued coloring of graph, using the new method, resulting in a number of new results,r-hued coloring and square coloring of some special graphs are studied in this paper. The main contents of the paper can be divided into the following three parts:The first section, this paper introduces background of the problem, the current research status and we are going to the content of the research.The second section, mainly on the Sierpiriski type graph r-hued coloring were studied, the Sierpiriski types of Graphs are introduced, the basic knowledge, finally, gives the concrete result and its proof.The third section, square coloring of semi-strong product of path and path, path and circle, circle and path and circle and circle, the first to introduce the relevant knowledge, the knowledge, finally gives the relevant results and proofs.