The unique minimizer of the distance spectral radius among connected graphs with m edges is the complement of a balanced disjoint union of paths.
Friedland, The maximal eigenvalue of 0-1 matrices with prescribed number of ones, Linear Algebra Appl
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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.