combinatorics / Spectral graph theory
If a finite graph has girth at least five, must its minimum dual degree satisfy $\delta^*(G) \le -\partial_n(G)$, where $\partial_n(G)$ is the smallest eigenvalue of its distance matrix? The Hoffman-Singleton graph violates it: dual degree $7$ against eigenvalue bound $4$.
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If a finite graph has girth at least five, must its minimum dual degree satisfy $\delta^*(G) \le -\partial_n(G)$, where $\partial_n(G)$ is the smallest eigenvalue of its distance matrix? The Hoffman-Singleton graph violates it: dual degree $7$ against eigenvalue bound $4$.
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If a finite graph has girth at least five, must its minimum dual degree satisfy $\delta^*(G) \le -\partial_n(G)$, where $\partial_n(G)$ is the smallest eigenvalue of its distance matrix? The Hoffman-Singleton graph violates it: dual degree $7$ against eigenvalue bound $4$.
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