Page 328 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 328
SPECTRAL GRAPH THEORY (MS-46)
[3] J.S. Fabila-Carrasco, F. Lledó and O. Post, Spectral gaps and discrete magnetic Lapla-
cians, Lin. Alg. Appl. 547 (2018) 183-216
Almost mixed Moore graphs and their spectra
Ignacio Lopez Lorenzo, nlopez@matematica.udl.es
Universitat de Lleida, Spain
Coauthor: Josep Maria Miret
Almost mixed Moore graphs appear in the context of the Degree/Diameter problem as a class
of extremal mixed graphs, in the sense that their order is one less than the Moore bound for
mixed graphs. In this talk we will give some necessary conditions for the existence of almost
mixed Moore graphs derived from the factorization in Q[x] of their characteristic polynomial.
In this context, we deal with the irreducibility of certain polynomials Φi(x) ◦ f (x), where Φi(x)
denotes the i-th cyclotomic polynomial.
Characterizing identifying codes from the spectrum of a graph or digraph
Berenice Martínez Barona, berenice.martinez@upc.edu
Universitat Politècnica de Catalunya, Spain
Coauthors: Camino Balbuena, Cristina Dalfó
A (1, ≤ )-identifying code in digraph D is a dominating subset C of vertices of D, such that all
distinct subsets of vertices of D with cardinality at most have distinct closed in-neighborhoods
within C. In this talk we give a new method to obtain an upper bound on for digraphs. The
results obtained here can also be applied to graphs. As far as we know, it is the first time that
the spectral graph theory has been applied to the identifying codes.
On some classes of signed graphs with small second largest eigenvalue
Bojana Mihailovic´, mihailovicb@etf.rs
University of Belgrade - School of Electrical Engineering, Serbia
In previous descriptions of some classes of maximal cacti for the property λ2 ≤ r (λ2 being
the second largest eigenvalue of the corresponding adjacency matrix), certain graph transfor-
mations that preserve the sign of λ2 − r have been used. Now, a possibility of applying such
transformations to some classes of signed graphs is examined, especially for r = 1.
326
[3] J.S. Fabila-Carrasco, F. Lledó and O. Post, Spectral gaps and discrete magnetic Lapla-
cians, Lin. Alg. Appl. 547 (2018) 183-216
Almost mixed Moore graphs and their spectra
Ignacio Lopez Lorenzo, nlopez@matematica.udl.es
Universitat de Lleida, Spain
Coauthor: Josep Maria Miret
Almost mixed Moore graphs appear in the context of the Degree/Diameter problem as a class
of extremal mixed graphs, in the sense that their order is one less than the Moore bound for
mixed graphs. In this talk we will give some necessary conditions for the existence of almost
mixed Moore graphs derived from the factorization in Q[x] of their characteristic polynomial.
In this context, we deal with the irreducibility of certain polynomials Φi(x) ◦ f (x), where Φi(x)
denotes the i-th cyclotomic polynomial.
Characterizing identifying codes from the spectrum of a graph or digraph
Berenice Martínez Barona, berenice.martinez@upc.edu
Universitat Politècnica de Catalunya, Spain
Coauthors: Camino Balbuena, Cristina Dalfó
A (1, ≤ )-identifying code in digraph D is a dominating subset C of vertices of D, such that all
distinct subsets of vertices of D with cardinality at most have distinct closed in-neighborhoods
within C. In this talk we give a new method to obtain an upper bound on for digraphs. The
results obtained here can also be applied to graphs. As far as we know, it is the first time that
the spectral graph theory has been applied to the identifying codes.
On some classes of signed graphs with small second largest eigenvalue
Bojana Mihailovic´, mihailovicb@etf.rs
University of Belgrade - School of Electrical Engineering, Serbia
In previous descriptions of some classes of maximal cacti for the property λ2 ≤ r (λ2 being
the second largest eigenvalue of the corresponding adjacency matrix), certain graph transfor-
mations that preserve the sign of λ2 − r have been used. Now, a possibility of applying such
transformations to some classes of signed graphs is examined, especially for r = 1.
326
