Isomorphic graphs I was wondering if this solution for finding wheter or not two graphs are isomorphic would work: I claim that two graphs are isomorphic if their degree list coincide. For example let's say that I have graphs A and B given by their adjacence matrix like so: $$ A = \begin{pmatrix} 0 & 1& 1 & 1 &0 \\\ 1 & 0& 0 & 0 &1 \\\ 1& 0 & 0 & 0 &0 \\\ 1& 0 & 0 & 0 &1 \\\ 0& 1 & 0 & 1 &0 \end{pmatrix} $$ $$B= \begin{pmatrix} 0 & 1 & 1 & 0 & 0\\\ 1 & 0 & 0 & 1 & 1\\\ 1 & 0 & 0 & 1 & 0\\\ 0 & 1 & 1 & 0 & 0\\\ 0 & 1 & 0 & 0 & 0 \end{pmatrix}$$ The degree list for A is 3,2,1,2,2 and for B is 2,3,2,2,1. This sets are equal. Therefore I say that A and B are isomorphic. If I am wrong, can you please explain me why is that with a counterexample

This graph has the same degree sequence as your $A$ and $B$, yet is not isomorphic to them:


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