The Study Of The Dynamic Coloring Of Graphs

In this dissertation, we introduce and study the idea of a dynamic coloring of a graph.A proper vertex k-coloring of a graph G is called dynamic,if there is no vertex v∈V （G） with d（v）≥2 and all of its neighbors have the same color. The smallest integer k such that G has a k-dynamic coloring is called the dynamic chromatic number of G and denoted by X₂ （G）. The dissertation is divided to four chapters.In the first chapter, we introduce the research background, current research status and basic definitions. Then, the topic of this article and the main work are briefly introduced.In the second chapter, we compare the chromatic number and dynamic chromatic number, and prove some upper bounds for X₂ （G）-χ （G） in terms of some parameters of the graph G. we prove the theorem by contradiction and induction and come to a conclusion thatIn the third chapter, the differences between X₂ （G） and X₂ （G-e）, and between X₂ （G） and X₂ （G-v） are investigated respectively, we prove that X₂ （G）-2≤ X₂（G-e）≤X₂ （G）+2 in the same way.In the fourth chapter, we make a summary of the above content and give some considerable problems for the further study.There are totaly 50 references in this paper.