On trees attaining the five largest ABS spectral radii

The atom-bond sum-connectivity (ABS) matrix of a graph G of order n is the square matrix of order n, whose (i, j)-entry is equal to (di + dj -2)/(di + dj) if the i-th vertex and the j-th vertex of G are adjacent, and 0 otherwise, where di is the degree of the i-th vertex of G.The ABS spectral radius of G is the largest eigenvalue of the ABS matrix of G.In this paper, the trees of order n with the first five largest ABS spectral radii are characterized.