A Number Of Parameters Research On Coloring Of Graphs

This dissertation is devoted to study the graph coloring problems. The coloring of graphs is one of the significant branches in graph theory. And in the discrete mathematics and combinatorial mathematics, the coloring problem has a wide range of applications. With the development of technology and their wide applications in reality, some new coloring concepts, such as total coloring, cycle coloring, strong edge coloring, star coloring, strong coloring , r-strong edge coloring and so on, have come forth in the latest decades. Since it is NP-complete to determine the vertex chromatic number and edge chromatic number of a general graph, it is also NP-complete to determine these generalized chromatic numbers. Thus, researchers mainly focus on some special classes of graphs and their various coloring problems.This dissertation consists of five chapters. Star coloring and 2-distance coloring of complete cubic Halin graphs, star coloring of Halin graphs, and r-strong edge coloring of a kind of graphs are investigated in this dissertation.In Chapter 1, we firstly introduced the development and application of the Graph theory, and gave some definitions and notations used throughout this dissertation.In Chapter 2, we gave a chief survey on graph coloring problems under consideration in this dissertation, and introduced what we mainly investigated in this dissertation.In Chapter 3, we investigated r-strong edge coloring of a kind of graphs, and got a better rang of r-strong edge coloring chromatic number.In Chapter 4, we investigated 2-distance coloring and star coloring of complete cubic Halin graphs, and star coloring of Halin graphs. We got a better rang of 2-distance coloring chromatic number and completely wonderful star chromatic number of complete cubic Halin graphs, at last, we got a better rang of star coloring chromatic number of Halin graphs.In Chapter 5, we gave the main results of this dissertation we devoted to study.