Distance spectral radius of series-reduced trees with parameters

Abstract

For a connected graph G, the distance matrix is a real-symmetric matrix where the (u, v)-entry is the distance between vertex u and vertex v in G. The distance spectral radius of G is the largest eigenvalue of the distance matrix of G. A series-reduced tree is a tree with at least one internal vertex and all internal vertices having degree at least three. Those series-reduced trees that maximize the distance spectral radius are determined over all series-reduced trees with fixed order and maximum degree and over all series-reduced trees with fixed order and number of leaves, respectively.