Graph Theory Is Becoming Increasingly Significant As It Is Applied to Many Areas of Science and Technology. It Is Being Actively Plays an Important In Many Areas, Such As Biochemistry (Genomics), Electrical Engineering (Communication Networks and Coding Theory), Computer Science (Algorithms and Computation) and Operations Research (Scheduling). the Commanding Combinatorial Methods Found In Graph Theory Have Also Been Used to Prove Fundamental Results In Other Areas of Pure Mathematics. In This Chapter, We Are Discus and Give a General Outline of Applications of Graph Theory In Science and Engineering.