The unique minimizer of the distance spectral radius among connected graphs with m edges is the complement of a balanced disjoint union of paths.
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2026 2verdicts
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The gap between 1/2 and the sum of squared Perron vector entries on an independent set can be exponentially small in graphs with arbitrarily large chromatic number, disproving two conjectures.
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On a conjecture of distance spectral extremal problems
The unique minimizer of the distance spectral radius among connected graphs with m edges is the complement of a balanced disjoint union of paths.
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An exponentially small gap of the Perron vector on independent sets
The gap between 1/2 and the sum of squared Perron vector entries on an independent set can be exponentially small in graphs with arbitrarily large chromatic number, disproving two conjectures.