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In this article, we determine the loops and neighborhoods of the vertices$E_{1728} \times E_{1728}$ and $E_0\times E_0$ (endowed with canonicalprincipal divisors) in the $(\ell,\ell)$-isogeny graph of principally polarizedsuperspecial abelian surfaces. We also present a simple new proof of the maintheorem in \cite{LOX20}.

Neighborhood of two vertices in the isogeny graph of principally polarized superspecial abelian surfaces