Answer:
The Swiss mathematician
Leonard Euler (1707  83) showed that the numbers of vertices (V),
edges (E) and faces (F) of a polyhedron satisfy the formula, V  E + F = 2
For example for a cube V = 8, E = 12 and F = 6, while for
a triangular prism V = 6, E = 9 and F = 5
A
similar formula applies to Networks,
N  A + R = 2. where N is the number of nodes, A the number
of arcs, and R the number of regions into which a network
divides the plane, including the region outside the network.
