two isimorphic graph determine the same partition
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Graph isomorphism
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(u) and f(v) are adjacent in H. ...
If an isomorphism exists between two graphs, then the graphs are called isomorphic and denoted as.
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