On graft transformations decreasing distance spectral radius of graphs

Abstract

The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. In this paper, we give several less restricted graft transformations that decrease the distance spectral radius, and determine the unique graph with minimum distance spectral radius among home-omorphically irreducible unicylic graphs on n ≥ 6 vertices, and the unique tree with minimum distance spectral radius among trees on n vertices with given number of vertices of degree two, respectively.