In the following, a general definition of the isomorphy relation for graphs
and specializations for simple hypergraphs (isomushgr) and simple
pseudographs (isomuspgr) are provided. The latter corresponds to the
definition in [Bollobas] p. 3). It is shown that the isomorphy relation for
graphs is an equivalence relation (isomgrref, isomgrsym, isomgrtr).
Fianlly, isomorphic graphs with different representations are studied
(strisomgrop, ushrisomgr).

Maybe more important than graph isomorphy is the notion of graph isomorphism,
which can be defined as in df-grisom. Then
resp. .
Notice that there can be multiple isomorphisms between two graphs (let
and
be two graphs with two vertices and one edge, then and
are two different isomorphisms between these graphs).

Another approach could be to define a category of graphs (there are maybe
multiple ones), where graph morphisms are couples consisting in a function on
vertices and a function on edges with required compatibilities, as used
in the definition of . And then, a graph isomorphism is defined as
an isomorphism in the category of graphs (something like "GraphIsom
= ( Iso ` GraphCat )" ). Then general category theory theorems could be
used, e.g., to show that graph isomorphy is an equivalence relation.