So I am a bit confused about the reduction between SAT, subgraph isomorphism (SI) and graph isomorphism (GI). I know that GI is in NP, and that SI is NP-complete. So I'm thinking if we can decide instances of SAT in polynomial time, then we can also solve GI and SI in polynomial time since SAT is NP-complete and if one NP-complete problem is solved, then all others are also solved.
Am I correct? Thank you!