1 Answers
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H
such that any two vertices u and v of G are adjacent in G if and only if f {\displaystyle f} and f {\displaystyle f} are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection.If an isomorphism exists between two graphs, then the graphs are called isomorphic and denoted as G ≃ H {\displaystyle G\simeq H}. In the case when the bijection is a mapping of a graph onto itself, i.e., when G and H are one and the same graph, the bijection is called an automorphism of G.If a graph is finite, we can prove it to be bijective by showing it is one-one/onto; no need to show both. Graph isomorphism is an equivalence relation on graphs and as such it partitions the class of all graphs into equivalence classes. A set of graphs isomorphic to each other is called an isomorphism class of graphs.
The two graphs shown below are isomorphic, despite their different looking drawings.
f = 6