ABSTRACT
It is no coincidence that graph theory has been independently discovered many times, since it may quite properly be regarded as an area of applied mathematics. Subsequent rediscoveries of graph theory by G. Kirchhoff and A. Cayley also had their roots in the physical world. L. Euler became the father of graph theory as well as topology when in 1736 he settled a famous unsolved problem of his day called the Konigsberg Bridge Problem. In proving that the problem is unsolvable, Euler replaced each land area by a point and each bridge by a line joining the corresponding points, thereby producing a "graph." Kirchhoff developed the theory of trees in 1847 in order to solve the system of simultaneous linear equations which give the current in each branch and around each circuit of an electric network. The most famous unsolved problem in graph theory and perhaps in all of mathematics is the celebrated Four Color Conjecture.
