Graph Theory is one of the trending domain of mathematics which has a great importance in the modern technology. The first concept about the Four Color problem was given by A.F.Mobius in his innovative speech in the year 1840. After that there be gan war of thoughts to solve the Four Colour problem. It was in the year 1852 when a genius student namely Francis Gutherie from university of London came with a positive solution but failed while applying the same in the four color problem. His brother Fr adric himself convinces that Francis was not satisfactory with the solution. Later many mathematicians like Kempe, Heawood, and Tait etc. tried their best to solve the problem but were unsuccessful. Finally, it was the year 1976 when Kenneth Appel and Wolfgang Haken proved conclusively the problem by means of computer.