TY - JOUR
T1 - Matching number, Hamiltonian graphs and magnetic Laplacian matrices
AU - Fabila-Carrasco, John Stewart
AU - Lledó, Fernando
AU - Post, Olaf
N1 - Funding Information:
JSFC and FLl were supported by Spanish Ministry of Economy and Competitiveness through project DGI MTM2017-84098-P , from the Severo Ochoa Programme for Centres of Excellence in R&D and from the Spanish National Research Council , through the Ayuda extraordinaria a Centros de Excelencia Severo Ochoa ( CEX2019-000904-S ).
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the underlying graph. In particular, we give a family of spectral obstructions parametrised by the magnetic potential for the graph to be matchable (i.e., having a perfect matching) or for the existence of a Hamiltonian cycle. We base our analysis on a special case of the spectral preorder introduced in [8], and we use the magnetic potential as a spectral control parameter.
AB - In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the underlying graph. In particular, we give a family of spectral obstructions parametrised by the magnetic potential for the graph to be matchable (i.e., having a perfect matching) or for the existence of a Hamiltonian cycle. We base our analysis on a special case of the spectral preorder introduced in [8], and we use the magnetic potential as a spectral control parameter.
KW - Discrete magnetic Laplacian
KW - Hamiltonian graph
KW - Matching number
KW - Spectral graph theory
UR - http://www.scopus.com/inward/record.url?scp=85124506003&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2022.02.006
DO - 10.1016/j.laa.2022.02.006
M3 - Article
AN - SCOPUS:85124506003
SN - 0024-3795
VL - 642
SP - 86
EP - 100
JO - Linear algebra and its applications
JF - Linear algebra and its applications
ER -