An **isomorphism** of graphs

such that any two vertices

This kind of bijection is commonly described as βedge-perserving bijectionβ.

If an isomorphism exists between two graphs, then the graphs are called **isomorphic** and denoted as

In case when the bijection is a maping of a graph onto itself, i.e. when **automorphism** of

Graph isomorphism is an equivalence relation on graphs and as such it partitions the class of all graphs into equivalance classes.