A Spectral Study of the Manhattan Networks |
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| Institution: | 1. University of Adelaide, Adelaide Business School, 10 Pulteney Street, Adelaide, SA 5000, Australia;2. Delft University of Technology, Faculty of Technology, Policy and Management, Jaffalaan 5, NL-2600, GA, Delft, Netherlands;3. University of Birmingham, Birmingham Business School, University House, Birmingham, B15 2TT, United Kingdom;4. RMIT University, School of Accounting, 445 Swanston Street, Melbourne, Victoria, 3000, Australia;5. Department of Taxation, College of Accounting Sciences, University of South Africa, Preller Street, Muckleneuk, Pretoria, South Africa;6. University of Glasgow, Adam Smith Business School, Glasgow, G12 8QQ, United Kingdom;1. The Institute for Manufacturing, University of Cambridge, Cambridge, United Kingdom;2. Nottingham University Business School, University of Nottingham, Nottingham, United Kingdom;3. School of Business and Management, Queen Mary College, University of London, London, United Kingdom |
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| 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. |
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