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A $t$-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most $t$.
An algebraic approach to the association schemes of coding theory
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Algebraic graph theory
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C. D. Godsil and B. D. McKay · 1980
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A. E. Brouwer, A. M. Cohen, and A. Neumaier · 1989
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On an infinite class of non-bipartite and non-Cayley graphs having 2-arc transitive automorphism groups
L. R. Nochefranca · 1991
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Completely regular codes
A. Neumaier · 1992
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Algebraic combinatorics
C. D. Godsil · 1993
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Geometric distance-regular covers
C. D. Godsil · 1993
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Euclidean representations and substructures of distance-regular graphs
J. H. Koolen · 1994
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Spectra of graphs. Theory and applications. 3rd edition
D. M. Cvetković, M. Doob, and H. Sachs · 1995
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Regular graphs with four eigenvalues
E. R. van Dam · 1995
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Linear algebra
P. Rowlinson · 1997
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The infinitude of 7-arc-transitive graphs
M. D. E. Conder and C. G. Walker · 1998
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The distance-regular graphs of valency four
A. E. Brouwer and J. H. Koolen · 1999
There are only finitely many distance-regular graphs of fixed valency greater than two
S. Bang, A. Dubickas, J. H. Koolen, and V. Moulton · 2009
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On k k -walk-regular graphs
C. Dalfó, M. A. Fiol, and E. Garriga · 2009
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On t t -cliques in k k -walk-regular graphs
C. Dalfó, M. A. Fiol, and E. Garriga · 2009
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Characterizing ( ℓ , m ) (\ell,m) -walk-regular graphs
C. Dalfó, M. A. Fiol, and E. Garriga · 2010
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On distance-regular graphs with smallest eigenvalue at least − m -m
J. H. Koolen and S. Bang · 2010
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On perturbations of almost distance-regular graphs
C. Dalfó, E. R. van Dam, and M. A. Fiol · 2011
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On a characterization of bilinear forms graphs
K. Metsch · 1999
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Nonexistence of some antipodal distance-regular graphs of diameter four
A. Juri s ˇ \check{\rm s} i c ´ \acute{\rm c} and J. Koolen · 2000
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Tight distance-regular graphs
A. Jurišić, J. Koolen, and P. Terwilliger · 2000
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An improvement of the Godsil bound
A. Hiraki and J. Koolen · 2002
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Symmetric cubic graphs of small girth
M. Conder and R. Nedela · 2007
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On almost distance-regular graphs
C. Dalfó, E. R. van Dam, M. A. Fiol, E. Garriga, and B. L. Gorissen · 2011
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On distance, geodesic and arc transitivity of graphs
A. Devillers, W. Jin, C. H. Li, and C. E. Praeger · 2011
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Spectral characterization of a graph on the flags of the eleven point biplane
A. Blokhuis and A. E. Brouwer · 2012
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An infinite family of biquasiprimitive 2-arc transitive cubic graphs
A. Devillers, M. Giudici, C. H. Li, and C. E. Praeger · 2012
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Corrections and additions to the book ‘Distance-regular Graphs’
A. E. Brouwer · 2013
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Distance-regular graphs
E. R. van Dam, J. H. Koolen, and H. Tanaka · 2013
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Cubic symmetric graphs (the Foster census)
G. Royle, M. Conder, B. McKay, and P. Dobscanyi · 2013
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