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Combinatorial designs with two singular values II. Partial geometric designs

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  • Dam, E.R. van

    (Tilburg University)

  • Spence, E.

Abstract

In this and an earlier paper [17] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize (v, k, ë) designs, and include uniform multiplicative designs and partial geometric designs.Here we study the latter, which are precisely the designs with constant replication and block size.We collect most known results, give new characterization results, and we enumerate, partly by computer, all small ones.

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-142650.

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Date of creation: 2005
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Publication status: Published in Linear Algebra and its Applications (2005) v.396, p.303-316
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-142650

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Web page: http://www.tilburguniversity.edu/

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  1. Dam, E.R. van & Caen, D. de & Spence, E., 1999. "A nonregular analogue of conference graphs," Open Access publications from Tilburg University urn:nbn:nl:ui:12-80216, Tilburg University.
  2. Dam, E.R. van, 1995. "Regular graphs with four eigenvalues," Open Access publications from Tilburg University urn:nbn:nl:ui:12-80122, Tilburg University.
  3. Dam, E.R. van & Spence, E., 1998. "Small regular graphs with four eigenvalues," Open Access publications from Tilburg University urn:nbn:nl:ui:12-76952, Tilburg University.
  4. Dam, E.R. van, 1998. "Nonregular graphs with three eigenvalues," Open Access publications from Tilburg University urn:nbn:nl:ui:12-76953, Tilburg University.
  5. Haemers, W.H. & Higman, D.G., 1989. "Strongly regular graphs with strongly regular decomposition," Open Access publications from Tilburg University urn:nbn:nl:ui:12-402393, Tilburg University.
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