An algebraic approach to lifts of digraphs
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We present some applications of a new matrix approach for studying the properties of the lift of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, we completely determine the spectrum of . As some examples of our technique, we
study some basic properties of the Alegre digraph, and completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and the Hoffman-Singleton graph
Is part ofDiscrete Applied Mathematics, 2019, vol. 269, p. 68-76
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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; 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 ...
Dalfó, Cristina; Fiol, Miguel Angel (Elsevier, 2019)We present a new matrix-based approach to detect and correct gross errors in GPS geodetic control networks. The study is carried out by introducing a new matrix, whose entries are powers of a (real or complex) variable, ...