Graph isomorphism
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to V(H)} such that any two vertices u and v of G are adjacent in G if and only if f ( u ) {\displaystyle f(u)} and f ( v ) {\displaystyle f(v)} 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. If an isomorphism exists between two graphs, then the graphs are called isomorphic, often denoted by G ≃ H {\displaystyle G\simeq H} .