Abstract
The connected graphs with least distance eigenvalues in [−2.383,0] and the trees with least distance eigenvalues in (−2−2,0] have been known. We determine the trees with least distance eigenvalues in [−3−5,−2−2] and the unicyclic and bicyclic graphs with least distance eigenvalues in (−2−2,−2.383). We also determine the trees with the kth largest least distance eigenvalues for every positive integer k up to 28, and the unicyclic and bicyclic graphs with the kth largest least distance eigenvalues respectively for any positive integer k.
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