On the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
| Autor: | Dalfó, C., Fiol, M. A., Pavlíková, S., Širáň, J. |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
| Rok vydání: | 2022 |
| Předmět: |
Algebras
Linear Lift Algebra and Number Theory Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal [Àrees temàtiques de la UPC] Grafs Teoria de 15 Linear and multilinear algebra matrix theory [Classificació AMS] 15 Linear and multilinear algebra [Classificació AMS] Eigenspace Eigen Space Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC] Mathematics::Spectral Theory Graph Graph theory matrix theory Universal adjacency matrix Àlgebra lineal Symmetric square 05 Combinatorics::05C Graph theory [Classificació AMS] |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Linear Multilinear Algebra |
| ISSN: | 1563-5139 0308-1087 |
| DOI: | 10.1080/03081087.2022.2042174 |
| Popis: | The universal adjacency matrix U of a graph Γ, with adjacency matrix A, is a linear combination of A, the diagonal matrix D of vertex degrees, the identity matrix I, and the all-1 matrix J with real coefficients, that is, U=c1A+c2D+c3I+c4J, with ci∈R and c1≠0. Thus, in particular cases, U may be the adjacency matrix, the Laplacian, the signless Laplacian, and the Seidel matrix. In this paper, we develop a method for determining the universal spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not). As an example, the method is applied to give an efficient algorithm to determine the characteristic polynomial of the Laplacian matrix of the symmetric squares of odd cycles, together with closed formulas for some of their eigenvalues. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922. The research of the two first authors is partially supported by AGAUR from the Catalan Government under project 2017SGR1087 and by MICINN from the Spanish Government under project PGC2018-095471-B-I00. The research of the first author has also been supported by MICINN from the Spanish Government under project MTM2017-83271-R. The third and fourth authors acknowledge support from the APVV Research Grants 15-0220 and 17-0428, and the VEGA Research Grants 1/0142/17 and 1/0238/19. |
| Databáze: | OpenAIRE |
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