A Spectral Study of the Manhattan Networks F. Comellas, C. Dalf´o, M. A. Fiol 1,2 Departament de Matem` atica Aplicada IV Universitat Polit` ecnica de Catalunya Barcelona, Spain M. Mitjana 1,3 Departament de Matem`atica Aplicada I Universitat Polit` ecnica de Catalunya Barcelona, Spain Abstract The multidimensional Manhattan networks are a family of digraphs with many appealing 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 fully 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: Manhattan Network, Spectra, Eigenvalues, Line digraph. 1 Research supported by the Secretaria de Estado de Universidades e Investigaci´ on (Min- isterio de Educaci´ on y Ciencia), Spain, and the European Regional Development Fund (ERDF) under projects MTM2005-08990-C02-01 and TEC2005-03575. 2 Email: {comellas,dalfo,fiol}@ma4.upc.edu 3 Email: margarida.mitjana@upc.edu Electronic Notes in Discrete Mathematics 29 (2007) 267–271 1571-0653/$ – see front matter © 2007 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2007.07.045