On least distance eigenvalues of trees, unicyclic graphs and bicyclic graphs

The connected graphs with least distance eigenvalues in [−2.383,0][−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.