On Radio Colorings And Hamiltonian Colorings Of Some Graphs

Graph colorings belong to classical graph theoretical problems. Graph coloring theory has a central position in discrete mathematics, and has plenty of theoretical results and extensively practical applications. In the latest years, a lot of research papers appeared in the field of restricted colorings of graphs. Restricted color-ings of graphs is a generalization of standard coloring of graphs. Radio colorings and Hamiltonian colorings of graphs are both of them. In the last decade, Radio colorings and Hamiltonian colorings of graphs have been becoming the hottest researching points for many scientists in the world scale. A large number of scien-tists of graph theory pay significant attention to Radio colorings and Hamiltonian colorings of some simple classes of graphs. In this paper, we researched some issue of Radio colorings and Hamiltonian colorings.This paper includes seven chapters:The first chapter is introduction, introduc-ing the phylogeny of graph theory, and the researching purpose and meanings of this paper; The second chapter is preparative knowledge. We give some infor-mation of graph and some concepts of graph; In the third chapter, we introduce the current situations and obtained consequences on Radio colorings and Hamil-tonian colorings; In the forth chapter, we discuss the proof of proof of antipodal chromatic number of paths,point out that there are several errors in the proof and give another correct proof; In the fifth chapter, we confirm the nearly antipodal chromatic number of even paths; In the sixth chapter, we confirm the Hamiltonian chromatic number of a class of generalized stars; In the last chapter, we sum up what we have done in this paper.