On trees with maximum algebraic connectivity-Reference-Cited by-同舟云学术

On trees with maximum algebraic connectivity

Published:2016 Issue:1 Volume:10 Page:88-101
ISSN:1452-8630
Container-title:Applicable Analysis and Discrete Mathematics
language:en
Short-container-title:APPL ANAL DISCRETE M

Author:

Abreu Nair¹,Markenzon Lilian²,Lee Luciana³,Rojo Oscar⁴

Affiliation:

1. Universidade Federal do Rio de Janeiro, Programa de Engenharia de Produção/COPPE, Rio de Janeiro, Brasil

2. Universidade Federal do Rio de Janeiro, Núcleo de Computação Eletrônica, Rio de Janeiro, Brasil

3. Universidade Federal do Espírito Santo, Centro Universitário Norte do Espírito Santo, Departamento de Computação e Eletrônica, Sâo Mateus, Brasil

4. Universidad Católica del Norte, Departamento de Matemáticas, Antofagasta, Chile

Abstract

In this paper, trees with fixed diameter and any number of vertices are investigated. A subclass of trees with diameter 2k is introduced, the diameter path trees (dp-trees). Two subclasses of dp-trees are defined in which we characterize the elements that maximize the algebraic connectivity. Also, it is proved that if any tree maximizes the algebraic connectivity over all trees with diameter 2k then it is a dp-tree. For such trees, a bound for the degrees of their vertices is given. In the case of the odd diameter, 2k-1, we show that P2k is the only tree that maximizes the algebraic connectivity.

Publisher

National Library of Serbia

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Trees with matrix weights: Laplacian matrix and characteristic-like vertices;Linear Algebra and its Applications;2022-08

2. Perron values and classes of trees;Linear Algebra and its Applications;2022-04

3. Relationships between algebraic connectivity and vertex connectivity;Computational and Applied Mathematics;2022-03-15

4. Perron value and moment of rooted trees;Linear Algebra and its Applications;2022-02

5. Locating the extremal entries of the Fiedler vector for rose trees;PAMM;2019-11