Isomorphic

Graphs $G$ and $H$ are isomorphic if there is an isomorphism between them: A function $f$ from the vertices of $G$ to the vertices of $H$ such that:

• $f$ is a bijection (function)

• $f$ takes edges to edges:

  For all vertices $x,y$ in $G$, if	Edges-to-edges (1) graph G {node[shape=point];x[xlabel="x"];y[xlabel="y"];y--x} Link to original	then	Edges-to-edges (2) graph G {node[shape=point];x[xlabel="f(x)"];y[xlabel="f(y)"];y--x} Link to original	in $H$.

• $f$ takes non-edges to non-edges:

  For all vertices $x,y$ in $G$, if	Non-edges-to-non-edges (1) graph G {node[shape=point];x[xlabel="x"];y[xlabel="y"]} Link to original	then	Non-edges-to-non-edges (2) graph G {node[shape=point];x[xlabel="f(x)"];y[xlabel="f(y)"]} Link to original	in $H$.