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<p>We present a new approach to the construction of strongly regular graphs that combines a genetic algorithm with a method based on a prescribed automorphism group. The construction relies on the use of orbit matrices, which are quotient matrices associated with equitable partitions of adjacency matrices of candidate strongly regular graphs, where the partitions are induced by the action of the prescribed group. By applying this hybrid method, we constructed new strongly regular graphs having parameters (96,&#xa0;19,&#xa0;2,&#xa0;4) and (96,&#xa0;20,&#xa0;4,&#xa0;4).</p>

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Using a genetic algorithm for construction of strongly regular graphs with a prescribed automorphism group

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Dean Crnković,
  • Tin Zrinski

摘要

We present a new approach to the construction of strongly regular graphs that combines a genetic algorithm with a method based on a prescribed automorphism group. The construction relies on the use of orbit matrices, which are quotient matrices associated with equitable partitions of adjacency matrices of candidate strongly regular graphs, where the partitions are induced by the action of the prescribed group. By applying this hybrid method, we constructed new strongly regular graphs having parameters (96, 19, 2, 4) and (96, 20, 4, 4).