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Developments on spectral characterizations of graphs

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  • Dam, E.R. van

    (Tilburg University)

  • Haemers, W.H.

    (Tilburg University)

Abstract

In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.2000 Mathematics Subject Classification: 05C50

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-3160873.

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Date of creation: 2009
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Publication status: Published in Discrete Mathematics (2009) v.309, p.576-586
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-3160873

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Web page: http://www.tilburguniversity.edu/

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  1. Dam, E.R. van & Koolen, J.H., 2004. "A New Family of Distance-Regular Graphs with Unbounded Diameter," Discussion Paper 2004-116, Tilburg University, Center for Economic Research.
  2. Dam, E.R. van & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
  3. Dam, E.R. van & Haemers, W.H. & Koolen, J.H., 2006. "Cospectral Graphs and the Generalized Adjacency Matrix," Discussion Paper 2006-31, Tilburg University, Center for Economic Research.
  4. Dam, E.R. van & Haemers, W.H. & Koolen, J.H. & Spence, E., 2005. "Characterizing Distance-Regularity of Graphs by the Spectrum," Discussion Paper 2005-19, Tilburg University, Center for Economic Research.
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Cited by:
  1. Dam, E.R. van & Haemers, W.H., 2010. "An Odd Characterization of the Generalized Odd Graphs," Discussion Paper 2010-47, Tilburg University, Center for Economic Research.
  2. Dalfo, C. & Dam, E.R. van & Fiol, M.A., 2011. "On perturbations of almost distance-regular graphs," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5013964, Tilburg University.
  3. Haemers, W.H. & Ramezani, F., 2009. "Graphs Cospectral with Kneser Graphs," Discussion Paper 2009-76, Tilburg University, Center for Economic Research.

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