Graph isomorphism

A graph isomorphism is a bijection between the vertices of two graphs $G$ and $H$ :

$f: V(G) \rightarrow V(H)$

with the property that any two vertices $u$ and $v$ from $G$ are adjacent if and only if $f (u)$ and $f (v)$ are adjacent in $H .$

If an isomorphism can be constructed between two graphs, then we say those graphs are isomorphic.

Determining whether two graphs are isomorphic is the graph isomorphism problem

Example

Consider these two graphs:

Although these graphs look very different, they are isomorphic; one isomorphism between them is

f (a) = 1

f (b) = 6

f (c) = 8

f (d) = 3

f (g) = 5

f (h) = 2

f (i) = 4

f (j) = 7