In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V → V {\displaystyle f\colon V\to V} such that any two vertices u and v of G are adjacent in G if and only if f {\displaystyle f} and f {\displaystyle f} are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection. Wikipedia