Injective Edge Coloring Of Graphs

All graphs considered in this paper are finite,simple,undirected graphs.Let G be a graph,we use V(G),E(G),δ(G),Δ(G)and mad(G)to denote its vertex set,edge set,minimum degree,maximum degree and maximum average degree.A k-injective coloring of G is a coloring of the vertices of G,f:V(G)→ C ={1,2,3,...,k},such that if any two vertices in G adjacent to the same neighbor,they receive distinct colors.xi(G)= min{k| G has a k-injective coloring}.A k-injective edge coloring of a graph G is a coloring,f:E(G)→ C = {1,2,3,…,k},such that if e1,e2 and e3 are consecutive edges in G,then f(e1)≠ f(e3).xi’(G)=min{k| G has a k-injective edge coloring} is called the injective edge coloring number.This master thesis,consisting of five chapters,focus on injective edge coloring on the graphs with different girth,maximum degree and maximum average degree as well as injective coloring on Halin graphs.In the first chapter,we introduce some definitions and give a brief survey of injective coloring(injective edge coloring).In the second chapter,we mainly discuss upper bound of Xi’(G)of some sparse graphs.In the third chapter,we mainly discuss upper bound of Xi’(G)of planar graphs with g(G)≥ 6.In the fourth chapter,we mainly discuss upper bound of Xi’(G)of some planar sparse graphs.In the fifth chapter,we mainly discuss upper bound of Xi(G)of Halin graphs.