Survey of polynomial transformations between NP-complete problems

This paper aims at being a guide to understand polynomial transformations and polynomial reductions between NP-complete problems by presenting the methodologies for polynomial reductions/transformations and the differences between reductions and transformations. To this end the article shows examples of polynomial reductions/transformations and the restrictions to reduce/transform between NP-complete problems. Finally, this paper includes a digraph with the historical reductions/transformations between instances of NP-complete problems and introduces the term family of polynomial transformations.