2.3 Mapping cyberspace over a visualization media
An exact match from the set to set is a mapping that has a corresponding relation tuple (element) in for each relation in . A mapping fulfilling this requirement is called a homomorphism from to such that
Consider that a mapping exists wherein there is a one-to-one correspondence between the vertices in and the vertices in a subgraph of such that a pair of vertices are adjacent in if and only if the corresponding pair of vertices are adjacent in the subgraph of . This is in fact the condition for a monomorphic mapping:
which can also be described as a isomorphic mapping to a subset from the relation such that
Note that all these morphism problems have been shown to be NP-complete and therefore cannot be solved exactly in polynomial time.