Distance-regular graphs

Abstract

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.

156 pages

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• Distance-regular graph with large a1 or c2
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Cited by in corpus (39)

• Eigenvalues of Cayley graphs
• Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk
• Max-cut and extendability of matchings in distance-regular graphs
• Strongly walk-regular graphs
• Entanglement of Free Fermions on Hadamard Graphs
• Dual Polar Graphs, a nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials
• Distance-regular Cayley graphs with least eigenvalue $-2$
• A compact presentation for the alternating central extension of the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• Nonsymmetric Askey-Wilson polynomials and $Q$-polynomial distance-regular graphs
• A characterization of Johnson and Hamming graphs and proof of Babai's conjecture
• Godsil-McKay switching and twisted Grassmann graphs
• Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs
• The Terwilliger algebra of the twisted Grassmann graph: the thin case
• Remarks on pseudo-vertex-transitive graphs with small diameter
• Multimarked Spatial Search by Continuous-Time Quantum Walk
• On the spectrum and linear programming bound for hypergraphs
• Distance-regular graphs with valency k having smallest eigenvalue at most -k/2
• A characterization of the graphs of bilinear $(d\times d)$-forms over ${\mathbb{F}}_2$
• Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters
• The uniqueness of a distance-regular graph with intersection array {32,27,8,1;1,4,27,32} and related results
• Grassmann graphs, degenerate DAHA, and non-symmetric dual $q$-Hahn polynomials
• Thick weakly distance-regular digraphs
• Characterizing graphs with fully positive semidefinite $Q$-matrices
• Equivalent characterizations of the spectra of graphs and applications to measures of distance-regularity
• Tight relative $t$-designs on two shells in hypercubes, and Hahn and Hermite polynomials
• Nonassociativity of the Norton Algebras of some distance regular graphs
• A spectral characterization of the s-clique extension of the square grid graphs
• On the coset graph construction of distance-regular graphs
• Twice $Q$-polynomial distance-regular graphs of diameter 4
• Speeding up finite-time consensus via minimal polynomial of a weighted graph - a numerical approach
• On the spectrum of two families of non-distance-regular graphs
• The super-connectivity of Johnson graphs
• Spectra of strongly Deza graphs
• A spectral characterization of the $s$-clique extension of the triangular graphs
• Primitive weakly distance-regular circulant digraphs
• A characterization of 2-neighborhood degree list of diameter 2 graphs
• On completely regular and completely transitive codes derived from Hamming codes
• On the automorphism groups of distance-regular graphs and rank-4 primitive coherent configurations
• On the Cheeger constant for distance-regular graphs