Definition:Isomorphism (Graph Theory)

Two graphs, $$G=(V(G),E(G))$$ and $$H=(V(H),E(H))$$ are isomorphic, denoted $$G\cong H$$, if there exists a bijection $$F:V(G)\to V(H)$$ such that for each edge $$\{u,v\}\in E(G)$$ there is an edge $$\{F(u),F(v)\}\in E(H)$$.

The function $$F$$ is called an isomorphism from $$G$$ to $$H$$.