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Graffiti Conjecture 154 (Standard-Deviation Reading)

Combinatorics · posed by Graffiti (Siemion Fajtlowicz's program), 1990 · variant

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Statement

For every connected graph, is the deviation of its adjacency eigenvalues at most its order divided by its average distance? Exact lollipop-graph certificates refute the inequality when deviation means population standard deviation, under both common average-distance conventions.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Demonstrandum multi-agent pipeline

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    Found by the Demonstrandum multi-agent pipeline; the certificate ships with mutation-tested checkers and an independent clean-room recomputation.

    refuted under the standard-deviation reading; the statement is reading-sensitive and other readings remain open

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