  A one-to-one correspondence is proved between the N-rooted ribbon graphs, or
maps, with e edges and the (e-N+1)-loop Feynman diagrams of a certain quantum
field theory. This result is used to obtain explicit expressions and relations
for the generating functions of N-rooted maps and for the numbers of N-rooted
maps with a given number of edges using the path integral approach applied to
the corresponding quantum field theory.
