See Graph theory

A (graph) isomorphism is a mapping between vertices of two graphs $G=(V_G, E_G)$ and $G'=(V_G', E_G')$ ($i \mapsto f(i)$ such that $i \in V_G$ and $j \in V_G'$) such that the edge $(i,j)$ is contained in the set of edges of $G$, if and only if the edge $(f(i), g(i))$ is contained in the set of edges of $G'$. To graphs are isomorphic if there exists an isomorphism between them. They are then also called "topologically equivalent".

Graph homomorphism means there is only implication of edge from domain to codomain