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Is there a notation for the statement $H$ is isomorphic to a subgraph of $G$? I was thinking of using $H<G$, but I'd like to use standard notation if possible.

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    $\begingroup$ I'm not sure, but it would rather suggest "$H$ is a proper subgraph of $G$". $H\le G$ might be closer to what you want (at least allowing $H=G$); I don't know if it's used in a distinct meaning. $\endgroup$
    – YCor
    Commented Mar 29, 2021 at 21:14

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Inspired by the $\simeq$ notation for isomorphic structures, I would suggest $\lesssim$, $\prec$, $\precsim$, or this symbol.

The pair of symbols $\prec$ and $\precsim$ have the advantage of providing a symbol for both allowing and discarding equality.

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    $\begingroup$ I'd interpret this as induced subgraph, as there seems to be a suggestion of morphism here. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Mar 29, 2021 at 23:14

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