dc.contributor
Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author
Dalfó Simó, Cristina
dc.contributor.author
Fiol Mora, Miquel Àngel
dc.date.issued
2020-07-15
dc.identifier
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.
dc.identifier
https://arxiv.org/pdf/1906.05851.pdf
dc.identifier
https://hdl.handle.net/2117/330465
dc.identifier
10.1016/j.laa.2020.03.015
dc.description.abstract
© 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/
dc.description.abstract
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.
dc.description.abstract
Peer Reviewed
dc.description.abstract
Postprint (author's final draft)
dc.format
application/pdf
dc.relation
https://www.sciencedirect.com/science/article/abs/pii/S0024379520301439?via%3Dihub
dc.relation
info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT
dc.relation
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./
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
dc.subject
Algebras, Linear
dc.subject
Lifted (di)graph
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Regular partition
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Symmetric group
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Representation theory
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New mixed graph
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Grafs, Teoria de
dc.subject
Àlgebra lineal
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Grups, Teoria de
dc.subject
Classificació AMS::05 Combinatorics::05C Graph theory
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Classificació AMS::15 Linear and multilinear algebra; matrix theory
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Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups
dc.title
Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups
