combinatorics / Spectral graph theory
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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refuted under the standard-deviation reading; the statement is reading-sensitive and other readings remain open
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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.
refuted under the standard-deviation reading; the statement is reading-sensitive and other readings remain open
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