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Graph theory

In solving the general problem of traversing graphs, Euler founded the branch of mathematics known as graph theory. Graphs arise in all sorts of situations. For example, the Schlegel diagram for a polyhedron forms a graph for which a variation of Euler’s formula holds: V – E + R = 1, where V, E and R denote respectively the number of vertices, edges, and internal regions of the graph.

For a tetrahedron: For a cube:
        
       
V = 4, E = 6, R = 3 V = 8, E = 12, R = 5