A New Upper Bound for the d-dimensional Algebraic Connectivity of Arbitrary Graphs

In this paper we show that the \(d\)-dimensional algebraic connectivity of an arbitrary graph \(G\) is bounded above by its \(1\)-dimensional algebraic connectivity, i.e., \(a_d(G) \leq a_1(G)\), where \(a_1(G)\) corresponds the well-studied second smallest eigenvalue of the graph Laplacian.

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-09
Main Authors: Presenza, Juan F, Mas, Ignacio, Giribet, Juan I, Alvarez-Hamelin, J Ignacio
Format: Article
Language:English
Subjects:
Algebra
Eigenvalues
Graph theory
Upper bounds
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we show that the \(d\)-dimensional algebraic connectivity of an arbitrary graph \(G\) is bounded above by its \(1\)-dimensional algebraic connectivity, i.e., \(a_d(G) \leq a_1(G)\), where \(a_1(G)\) corresponds the well-studied second smallest eigenvalue of the graph Laplacian.
ISSN:2331-8422