Star Coloring And Strong Edge Coloring Of Graphs

The coloring problem is one of the important problems in the graph theory. In the discrete mathematics and combinatorial analysis, the coloring problem has a wide range of applications. The problem are closely related to coloring theory in many different areas. For example, scheduling, time-table probem, the problem of storing, and so on. In this paper, we mainly study the star coloring of low degree graphs and the strong edge coloring of planar graphs. The concrete results are as follows.Firstly, we summarize the current research on coloring of general graph and related basic concepts. For example, vertex coloring, star coloring, edge coloring and strong edge coloring.Secondly, in the article, it's introduced the concept of star coloring and strong edge coloring.Finally, depending on the structure of low degree graph and planar graph, we found the star chromatic number of a class of low degree graphs and proved that the strong edge coloring of a class of planar graphs satisfied strong edge coloring conjecture by construction methods.