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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation> be a nontrivial Steiner design admitting a group <i>G</i> of automorphisms. In this paper, we study (<i>G</i>,&#xa0;<i>s</i>)-flag-transitivity of Steiner designs. We firstly present a complete classification of (<i>G</i>,&#xa0;<i>s</i>)-flag-transitive Steiner <i>t</i>-designs for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1\le s\le t\le 5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>s</mi> <mo>≤</mo> <mi>t</mi> <mo>≤</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>. Then we construct some new families of semisymmetric graphs from (<i>G</i>,&#xa0;<i>s</i>)-flag-transitive Steiner designs.</p>

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On s-flag-transitive designs and semisymmetric graphs

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Zheng Huang,
  • Weijun Liu,
  • Qian-Fen Liao,
  • Li-Hua Feng,
  • Wei Jin

摘要

Let \(\mathcal {D}\) D be a nontrivial Steiner design admitting a group G of automorphisms. In this paper, we study (G, s)-flag-transitivity of Steiner designs. We firstly present a complete classification of (G, s)-flag-transitive Steiner t-designs for \(1\le s\le t\le 5\) 1 ≤ s ≤ t ≤ 5 . Then we construct some new families of semisymmetric graphs from (G, s)-flag-transitive Steiner designs.