Abstract
In this paper we study the absolute values of non-trivial eigenvalues of a distance-regular graph and find that these usually have large absolute value. We also give a motivation concerning a conjecture of Bannai and Ito.
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E. Bannai T. Ito (1987) ArticleTitleThe study of distance-regular graphs from the algebraic (i.e. character theoretical) viewpoint Proceedings of Symposia in Pure Mathematics 47 343–349
Norman Biggs, Algebraic Graph Theory, Second edition, Cambridge University Press, Cambridge, (1993).
A. E. Brouwer A. M. Cohen A. Neumaier (Eds) (1989) Distance-Regular Graphs Springer-Verlag Berlin
C. D. Godsil (Eds) (1993) Algebraic Combinatorics, Chapman and Hall Mathematics Series Chapman and Hall New York
H. Haemers Willem (1995) ArticleTitleInterlacing Eigenvalues and Graphs Linear Algebra and Application 226/228 593–616
A. A. Ivanov (1983) ArticleTitleBounding the diameter of a distance-regular graph (Russian) Dokl. Akad. Nauk SSSR 271 789
P. Terwilliger (1982) ArticleTitleEigenvalue multiplicities of highly symmetric graphs Discrete Mathmatics 41 295–302
P. Terwilliger (1983) ArticleTitleDistance-regular graphs and (s,a,c,k)-graphs J. Combinatorial Theory (B) 34 151–164
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Sejeong, B., Koolen, J.H. Some Interlacing Results for the Eigenvalues of Distance-regular graphs. Des Codes Crypt 34, 173–186 (2005). https://doi.org/10.1007/s10623-004-4853-8
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DOI: https://doi.org/10.1007/s10623-004-4853-8