engleski

Strongly regular graphs with parameters (81,30,9,12) and a new partial geometry

In this talk we will explain the method for constructing strongly regular graphs. Using the method, twelve new strongly regular graphs with parameters (81, 30, 9, 12) are found as graphs invariant under certain subgroups of the automorphism groups of the two previously known graphs that arise from 2-weight codes. One of these new graphs is geometric and yields a partial geometry with parameters pg(5, 5, 2) that is not isomorphic to the partial geometry discovered by J. H. van Lint and A. Schrijver [2] in 1981. The talk is based on the recent work given in [1]. References [1] D. Crnković, A. Švob, V. D. Tonchev, Strongly regular graphs with parameters (81, 30, 9, 12) and a new partial geometry, ArXiv preprint, https://arxiv.org/pdf/2009.09544 [2] J. H. van Lint, A. Schrijver, Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields, Combinatorica 1 (1981), 63–73.

partial geometry ; strongly regular graphs

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