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The spectra of Manhattan street networks
Authors:F Comellas
Institution:a Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Barcelona, Catalonia, Spain
b Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Catalonia, Spain
Abstract:The multidimensional Manhattan street networks constitute a family of digraphs with many interesting properties, such as vertex symmetry (in fact they are Cayley digraphs), easy routing, Hamiltonicity, and modular structure. From the known structural properties of these digraphs, we determine their spectra, which always contain the spectra of hypercubes. In particular, in the standard (two-dimensional) case it is shown that their line digraph structure imposes the presence of the zero eigenvalue with a large multiplicity.
Keywords:05C50  05C28
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