The integral trees with spectral radius 3

The integral trees with spectral radius 3

There are 11 integral trees with largest eigenvalue 3.

The Dirichlet spectral radius of trees

In this paper, the trees with the largest Dirichlet spectral radius among all trees with a given degree sequence are characterized. Moreover, the extremal graphs having the largest Dirichlet spectral radius are obtained in the set of all trees of order n with a given number of pendant vertices.

Trees with given maximum degree minimizing the spectral radius

The spectral radius of a graph is the largest eigenvalue of the adjacency matrix of the graph. Let T (n,∆, l) be the tree which minimizes the spectral radius of all trees of order n with exactly l vertices of maximum degree ∆. In this paper, T (n,∆, l) is determined for ∆ = 3, and for l ≤ 3 and n large enough. It is proven that for sufficiently large n, T (n, 3, l) is a caterpillar with (almost...

Ela Distance Spectral Radius of Trees with Fixed Maximum Degree∗

Abstract. Distance energy is a newly introduced molecular graph-based analog of the total π-electron energy, and it is defined as the sum of the absolute eigenvalues of the molecular distance matrix. For trees and unicyclic graphs, distance energy is equal to the doubled value of the distance spectral radius. In this paper, we introduce a general transformation that increases the distance spect...

Distance spectral radius of trees with fixed maximum degree