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

Juan F. Presenza; Ignacio Mas; Juan I. Giribet; J. Ignacio Alvarez-Hamelin

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

Combinatorics 2022-09-30 v1 Algebraic Geometry

Authors: Juan F. Presenza , Ignacio Mas , Juan I. Giribet , J. Ignacio Alvarez-Hamelin

Abstract

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.

Keywords

graph connectivity graph laplacian spectral graph theory

Cite

@article{arxiv.2209.14893,
  title  = {A New Upper Bound for the d-dimensional Algebraic Connectivity of Arbitrary Graphs},
  author = {Juan F. Presenza and Ignacio Mas and Juan I. Giribet and J. Ignacio Alvarez-Hamelin},
  journal= {arXiv preprint arXiv:2209.14893},
  year   = {2022}
}

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