Spectra and eigenspaces of arbitrary lifts of graphs
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We describe, in a very explicit way, a method for determining the spec-tra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regularor not).
Is part ofActa Mathematica Universitatis Comenianae, 2019, vol. LXXXVIII, num. 3, p. 593-600
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Dalfó, Cristina; Fiol, Miguel Angel (International Linear Algebra Society, 2020-07-12)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 ...
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 ...
The spectral excess theorem for graphs with few eigenvalues whose distance- 2 or distance-1-or-2 graph is strongly regular Dalfó, Cristina; Fiol, Miguel Angel; Koolen, Jack (Taylor & Francis, 2018-07-13)We study regular graphs whose distance-2 graph or distance-1-or-2 graph is strongly regular. We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and ...