Further results on the distance spectral radius of graphs

摘要

Let D(G) be the distance matrix of a connected graph G. The distance spectral radius of G is the largest eigenvalue of D(G) and it has been proposed to be a molecular structure descriptor. In this article, we determine the unique trees with minimal and maximal distance spectral radii among trees with fixed bipartition. As a corollary, the trees with the first three minimal distance spectral radii are determined. Furthermore, we determine the unique trees with minimal distance spectral radii among n-vertex trees with fixed number of pendent vertices or fixed even diameter, respectively. We also propose a conjecture regarding the tree with minimal distance spectral radius among n-vertex trees with fixed odd diameter.