  The presented material is devoted to the equivalent conversion from the
vertex graphs to the edge graphs. We suggest that the proved theorems solve the
problem of the isomorphism of graphs, the problem of the graph's enumeration
with the help of the effective algorithms without their preliminary plotting,
etc. The examining of the transformation of the vertex graphs into the edge
graph and the opposite operation illustrates the reasons of the appearance of
the NP-completeness from the point of view of the graph theory. We suggest that
it also illustrates the synchronous possibility and impossibility of the
struggle with the NP-completeness.
