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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.

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owne and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediate and investigate your claim.

General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research-You may not further distribute the material or use it for any profit-making activity or commercial gain-You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.

We study nonregular graphs with three eigenvalues. We determine all the ones with least eigenvalue &2, and give new infinite families of examples. 1998Academic Press

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In the area of computer simulation, Latin hypercube designs play an important role. In this paper the classes of maximin and Audze-Eglais Latin hypercube designs are considered. Up to now only several two-dimensional designs and a few higher dimensional designs for these classes have been published. Using periodic designs and the Enhanced Stochastic Evolutionary algorithm of Jin et al. (J. Stat. Plan. Interference 134(1):268-687, 2005), we obtain new results which we compare to existing results. We thus construct a database of approximate maximin and Audze-Eglais Latin hypercube designs for up to ten dimensions and for up to 300 design points. All these designs can be downloaded from the website http://www.spacefillingdesigns.nl.

Distance-regular graphs are a key concept in Algebraic Combinatorics\ud and have given rise to several generalizations, such as association\ud schemes. Motivated by spectral and other algebraic characterizations\ud of distance-regular graphs, we study ‘almost distanceregular\ud graphs’. We use this name informally for graphs that share\ud some regularity properties that are related to distance in the graph.\ud For example, a known characterization of a distance-regular graph\ud is the invariance of the number of walks of given length between\ud vertices at a given distance, while a graph is called walk-regular if\ud the number of closed walks of given length rooted at any given vertex\ud is a constant. One of the concepts studied here is a generalization\ud of both distance-regularity and walk-regularity called m-walkregularity.\ud Another studied concept is that of m-partial distanceregularity\ud or, informally, distance-regularity up to distance m. Using\ud eigenvalues of graphs and the predistance polynomials, we discuss\ud and relate these and other concepts of almost distance-regularity,\ud such as their common generalization of ( ,m)-walk-regularity. We\ud introduce the concepts of punctual distance-regularity and punctual\ud walk-regularity as a fundament upon which almost distanceregular\ud graphs are built. We provide examples that are mostly\ud taken from the Foster census, a collection of symmetric cubic\ud graphs. Two problems are posed that are related to the question of\ud when almost distance-regular becomes whole distance-regular. We\ud also give several characterizations of punctually distance-regular\ud graphs that are generalizations of the spectral excess theorem.Postprint (published version