Necessities for two undirected graphs being isomorphic As far as I know, for two undirected graphs $G = (V, E) $ and $H = (V', E')$, the following criteria is necessary for them to be isomorphic:


$|V| = |V'|$
$|E| = |E'|$
$G$ has $j$ nodes of degree $k$ $\Leftrightarrow $ $H$ has $j$ nodes of degree $k$


Are there more that are that obvious? Thanks in advance for your help!
For two graphs $G$ and&nbsp;$H$ it is necessary for literally every property that holds of&nbsp;$G$ to also hold of&nbsp;$H$ and vice-versa.  There's no point making a list because everything is in that list.