caa a22 4500 445886579 CHVBK 20180317145601.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s11128-010-0205-y doi (NATIONALLICENCE)springer-10.1007/s11128-010-0205-y Quantum walks, Ihara zeta functions and cospectrality in regular graphs [Elektronische Daten] [Peng Ren, Tatjana Aleksić, David Emms, Richard Wilson, Edwin Hancock] In this paper we explore an interesting relationship between discrete-time quantum walks and the Ihara zeta function of a graph. The paper commences by reviewing the related literature on the discrete-time quantum walks and the Ihara zeta function. Mathematical definitions of the two concepts are then provided, followed by analyzing the relationship between them. Based on this analysis we are able to account for why the Ihara zeta function can not distinguish cospectral regular graphs. This analysis suggests a means by which to develop zeta functions that have potential in distinguishing such structures. Springer Science+Business Media, LLC, 2010 Quantum walks nationallicence Ihara zeta functions nationallicence Cospectrality nationallicence Ren Peng Department of Computer Science, The University of York, YO10 5DD, York, UK aut Aleksić Tatjana Faculty of Science, University of Kragujevac, 34000, Kragujevac, Serbia aut Emms David Department of Computer Science, The University of York, YO10 5DD, York, UK aut Wilson Richard Department of Computer Science, The University of York, YO10 5DD, York, UK aut Hancock Edwin Department of Computer Science, The University of York, YO10 5DD, York, UK aut Quantum Information Processing Springer US; http://www.springer-ny.com 10/3(2011-06-01), 405-417 1570-0755 10:3<405 2011 10 11128 https://doi.org/10.1007/s11128-010-0205-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11128-010-0205-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ren Peng Department of Computer Science, The University of York, YO10 5DD, York, UK aut NATIONALLICENCE 700 1- Aleksić Tatjana Faculty of Science, University of Kragujevac, 34000, Kragujevac, Serbia aut NATIONALLICENCE 700 1- Emms David Department of Computer Science, The University of York, YO10 5DD, York, UK aut NATIONALLICENCE 700 1- Wilson Richard Department of Computer Science, The University of York, YO10 5DD, York, UK aut NATIONALLICENCE 700 1- Hancock Edwin Department of Computer Science, The University of York, YO10 5DD, York, UK aut NATIONALLICENCE 773 0- Quantum Information Processing Springer US; http://www.springer-ny.com 10/3(2011-06-01), 405-417 1570-0755 10:3<405 2011 10 11128 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer