Laplacian spectral radius of trees with given maximum degree

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

The signless Laplacian spectral radius of graphs with given degree sequences

The Laplacian spectral radius of graphs with given matching number

In this paper, we show that of all graphs of order n with matching number β, the graphs with maximal spectral radius are Kn if n = 2β or 2β + 1; K2β+1 ∪Kn−2β−1 if 2β + 2 n < 3β + 2; Kβ ∨ Kn−β or K2β+1 ∪Kn−2β−1 if n = 3β + 2; Kβ ∨ Kn−β if n > 3β + 2, where Kt is the empty graph on t vertices. © 2006 Elsevier Inc. All rights reserved. AMS classification: 05C35; 05C50