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Strongly regular configurations

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Abstract

We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed. Necessary existence conditions are proved and a table of feasible parameters of such configurations with at most 200 points is presented. Non-existence of some configurations with feasible parameters is proved.

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Notes

  1. We will always use the term line graph in this sense, and not in the sense of graph theory (the line graph L(G) of a graph G).

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Authors and Affiliations

  1. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano 10, Potenza, Italy

    Marién Abreu, Martin Funk & Domenico Labbate

  2. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Vedran Krčadinac

Authors
  1. Marién Abreu
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  2. Martin Funk
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  3. Vedran Krčadinac
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  4. Domenico Labbate
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Correspondence to Vedran Krčadinac.

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Communicated by D. Ghinelli.

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Vedran Krčadinac was supported by the Croatian Science Foundation under the Projects 6732 and 9752.

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Abreu, M., Funk, M., Krčadinac, V. et al. Strongly regular configurations. Des. Codes Cryptogr. 90, 1881–1897 (2022). https://doi.org/10.1007/s10623-022-01080-w

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