A general method to obtain the spectrum and local spectra of a graph from its regular partitions
MetadataShow full item record
It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also the local spectra, of a graph from the quotient matrices of some of its regular partitions, is proposed. Moreover, from such partitions, the C-local multiplicities of any class of vertices C is also determined, and some applications of these parameters in the characterization of completely regular codes and their inner distributions are described. As examples, it is shown how to find the eigenvalues and (local) multiplicities of walk-regular, distance-regular, and distance-biregular graphs.
Is part ofElectronic Journal Of Linear Algebra, 2020, vol. 36, num. 36, p. 446-460
European research projects
Showing items related by title, author, creator and subject.
Dalfó, Cristina; Fiol, Miguel Angel; Sirán, Jozef (Springer, 2019-01-02)We present a method to derive the complete spectrum of the lift Γα of a base digraph Γ , with voltage assignment α on a (finite) group G. The method is based on assigning to Γ a quotient-like matrix whose entries are ...
Dalfó, Cristina; Duque, F.; Fabila Monroy, R.; Fiol, Miguel Angel; Huemer, Clemens; Zaragoza Martínez, F.J.; Trujillo Negrete, A.L. (Elsevier, 2021)We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph Fk(G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent ...
Dalfó, Cristina; Fiol, Miguel Angel (Elsevier, 2020)In this paper, we present a method to obtain regular (or equitable) partitions of Cayley (di)graphs (that is, graphs, digraphs, or mixed graphs) of permutation groups on n letters. We prove that every partition of the ...