The 1-2-3 Conjecture On Edge Coloring Of Some Special Graphs

In 2004,Karo?nski,?uczak and Thomason conjectured that every connected graph of order greater than 2 has a neighbour-distinguishing edge labeling in {1,2,3},which is also called 1-2-3 conjecture.This thesis investigates the 1-2-3 conjecture on the edge coloring of trees,grid graphs and some generalized Petersen graphs.We prove that the1-2-3 conjecture is true for these graphs by using mathematical induction and labeling methods.