Star Edge Coloring Of Some Special Graphs

It is very meaningful to study the edge coloring of graphs.Scholars national and abroad have done a lot of research work to determine the chromatic index of graphs.In 2008,Liu et al.introduced the concept of star edge coloring of graphs,a star edge coloring of graph G is a proper edge coloring of graph G such that any path or cycle of length 4 in graph G is not bicolored.The star chromatic index of graph G is denoted by X’st(G)The acyclic edge coloring of graph and the strong edge coloring of graph have close relations to the star edge coloring of graph:the acyclic chromatic index of graph G is less than the star chromatic index of graph G,the star chromatic index of graph G is less than the strong chromatic index of graph G.Therefore,it is very meaningful to study the star edge coloring of graphs.In this thesis,we study the star chromatic index of Halin graph,power of k graph and the generalized Petersen graph P(3n,n),this thesis is divided into five chapters.In chapter 1,we introduce the origin of star edge coloring,expound the concepts and symbols that will be used in this thesis and list s’ome theorems to be used throughout the thesis.In chapter 2,we prove that 4≤χ’st(G)≤6,where the Halin graph is a cubic Halin graph.Next,we prove that 4≤χ’st(G)≤5,where the Halin graph is a necklace.Finally,we prove that χ’st(G)≤[3Δ/2]＋1,where the Halin graph is a complete Halin graph withΔ(G)≥6.In chapter 3,we prove that X’st(Pn2)=-(n≥5).Next,we show that the upper bound and the lower bound of the star chromatic index of graph Pnk.Finally,we prove that χ’st(Cn2)≤9.In chapter 4,we prove that χ’st(P(3n,n))=5,n≥2.In chapter 5,we summarize the thesis and give some topics for further research.