3 problems

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Linear exceptional-eigenvalue count conjecture for Markoff graphs
Exceptional-eigenvalue count conjecture. The exponent is $\alpha=1$ ; in particular, the number of such large eigenvalues is of order $p$ , and these eigenvalues form a vanishing pro…
Conjectureopeneigenvalues markoff-surface spectral-graph-theoryarXiv posted 2 days ago
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Limit conjecture for Markoff graph eigenvalues when p is 1 modulo 4
Eigenvalue limit conjecture. If $p\equiv 1\pmod 4$ , then $\lambda_2(p)$ converges to a limit $L$ satisfying
Conjectureopenfinite-graphs markoff-surface spectral-graph-theoryarXiv posted 2 days ago
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Asymptotic Ramanujan conjecture for Markoff graphs when p is 3 modulo 4
Asymptotic Ramanujan conjecture. If $p\equiv 3\pmod 4$ , then $G_p$ is asymptotically Ramanujan; equivalently,
Conjectureopenmarkoff-surface ramanujan-graphs spectral-graph-theoryarXiv posted 2 days ago

Linear exceptional-eigenvalue count conjecture for Markoff graphs