2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58570A graph G is called "minimalizable" if a diagram with minimal crossing number can be obtained from an arbitrary diagram of G by crossing changes. If, furthermore, the minimal diagram is unique up to crossing changes then G is called "strongly minimalizable". In this article, it is explained how minimalizability of a graph is related to its automorphism group and it is shown that a graph is strongly minimalizable if the automorphism group is trivial or isomorphic to a product of symmetric groups. Then, the treatment of crossing number problems in graph theory by knot theoretical means is discussed and, as an example, a planarity criterion for minimalizable graphs is given.14 pages, 9 figures, latex2e, metafont; Theorems 1 and 7 modified, example and lemma 11 added; definition clarified and minor correctionsGeometric TopologyCombinatorics05C10; 57M15text