Subgraph isomorphism (SI) detection is an important problem for several computer science subfields. In this paper we present a study of the subgraph isomorphism problem (SIP) and its relation with the Hamiltonian cycles and SAT problems. In particular, we describe how instances of those problems can be solved throughout SI detection (using problems reductions). In our experiments we use an algorithm developed by the authors, which is capable to find all valid mappings in a SI instance. We performed several experiments, including cases for which there exists a known solution in polynomial time. In our analysis, we show the advantage and disadvantage of using a SI representation to solve Hamiltonian cycles and SAT problems