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We show that any connected regular graph with $d+1$ distinct eigenvalues and odd-girth $2d+1$ is distance-regular, and in particular that it is a generalized odd graph.
D.M. Cvetković, M. Doob, and H. Sachs,
1980
Earlier work this paper cites.
A.E. Brouwer, A.M. Cohen, and A. Neumaier,
1989
Earlier work this paper cites.
M.A. Fiol and E. Garriga, From local adjacency polynomials to locally pseudo-distance-regular graphs
1997
Earlier work this paper cites.
E.R. van Dam and W.H. Haemers, Graphs with constant
1998
Earlier work this paper cites.
T. Huang and C. Liu, Spectral characterization of some generalized odd graphs
1999
Cited alongside, same era.
M.A. Fiol, Algebraic characterizations of distance-regular graphs
2002
Cited alongside, same era.
E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?
2003
Cited alongside, same era.
E.R. van Dam, W.H. Haemers, J.H. Koolen, and E. Spence, Characterizing distance-regularity of graphs by the spectrum
2006
Cited alongside, same era.
E.R. van Dam, The spectral excess theorem for distance-regular graphs: a global (over)view
2008
Later among the works it cites.
E.R. van Dam and W.H. Haemers, Developments on spectral characterizations of graphs
2009
Later among the works it cites.
M.A. Fiol, S. Gago, and E. Garriga, A simple proof of the spectral excess theorem for distance-regular graphs
2010
Later among the works it cites.
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