Facultad de Ciencias

Seminario: "Isospectral graphs for the discrete magnetic Laplacian"

Ponente

Fernando Lledó Macau

Institución de origen

Departamento de Matemáticas

Fecha

22-10-2021

Hora

11:30 h

Lugar

Aula Naranja, ICMAT y además on line

Descripción

URL: https://us06web.zoom.us/j/5446648029

Resumen:
Analysis on graphs studies the connections between geometrical or combinatorial
properties of graphs and natural operators defined on them. In this talk,
I will present a new geometrical construction leading to an infinite collection
of families of graphs, where all the elements in each family are (finite) isospectral
non-isomorphic graphs for the discrete magnetic Laplacian with standard
weights. The construction is based on the notion of isospectral frames which,
together with the s-partition of a natural number r, define the isospectral families
of graphs by contraction of distinguished vertices. The isospectral frames
have high symmetry and we use a spectral preorder of graphs studied in [2,3]
to control the spectral spreading of the eigenvalues under elementary perturbations
of the graph like vertex contraction and vertex virtualisation.

References:
[1] J.S. Fabila-Carrasco, F. Lled ´o and O. Post, A geometric construction of
isospectral magnetic graphs, 2021 (in preparation).
[2] J.S. Fabila-Carrasco, F. Lled ´o and O. Post, Spectral preorder and perturbations
of discrete weighted graphs, Math. Ann. 2020,
DOI: https://doi.org/10.1007/s00208-020-02091-5
[3] J.S. Fabila-Carrasco, F. Lled ´o and O. Post, Spectral gaps and discrete
magnetic Laplacians, Lin. Alg. Appl. 547 (2018) 183-216
ICMAT CSIC-UAM-UC3M-UCM
Departamento de Matem´ aticas. U.A.M.

Observaciones