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- W2953300260 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 $P(n)$ and to a recent known family of mixed graphs $Gamma(d,n,r)$ (having edges with and without direction). As a byproduct, the existence of perfect codes in $P(n)$ allows us to give a lower bound for the multiplicity of its eigenvalue $-1$." @default.
- W2953300260 created "2019-06-27" @default.
- W2953300260 creator A5031744770 @default.
- W2953300260 creator A5078943135 @default.
- W2953300260 date "2019-06-13" @default.
- W2953300260 modified "2023-10-16" @default.
- W2953300260 title "Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups" @default.
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- W2953300260 doi "https://doi.org/10.48550/arxiv.1906.05851" @default.
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