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oai:recercat.cat:2117/3304652026-01-16T09:54:45Zcom_2072_1033col_2072_452950

Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups Dalfó Simó, Cristina Fiol Mora, Miquel Àngel Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups Graph theory Algebras, Linear Group theory Lifted (di)graph Regular partition Spectrum Symmetric group Representation theory Pancake graph New mixed graph Grafs, Teoria de Àlgebra lineal Grups, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::15 Linear and multilinear algebra; matrix theory Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 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 number n gives rise to a regular partition of the Cayley graph. By using representation theory, we also obtain the complete spectra and the eigenspaces of the corresponding quotient (di)graphs. More precisely, we provide a method to find all the eigenvalues and eigenvectors of such (di)graphs, based on their irreducible representations. As examples, we apply this method to the pancake graphs and to a recent known family of mixed graphs (having edges with and without direction). As a byproduct, the existence of perfect codes in allows us to give a lower bound for the multiplicity of its eigenvalue -1. Peer Reviewed Postprint (author's final draft) 2020-07-15 Article Dalfo, C.; Fiol, M. Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups. "Linear algebra and its applications", 15 Juliol 2020, vol. 597, p. 94-112. 0024-3795 https://arxiv.org/pdf/1906.05851.pdf https://hdl.handle.net/2117/330465 10.1016/j.laa.2020.03.015 eng https://www.sciencedirect.com/science/article/abs/pii/S0024379520301439?via%3Dihub info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095471-B-I00/ES/ESTUDIO MATEMATICO DE LOS FALLOS EN CASCADA EN SISTEMAS COMPLEJOS MEDIANTE INVARIANTES Y CENTRALIDADES EN GRAFOS. APLICACIONES A REDES REALES./ Open Access 19 p. application/pdf Elsevier