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<p>In this paper, we classify directed strongly regular graphs admitting a transitive action of one of the linear groups <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_703_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="94" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_2(q), q\le 32\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_703_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_3(q), q \le 7\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="200_2025_703_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_4(2)\)</EquationSource> </InlineEquation>, for which the rank of the permutation representation is at most 20. Several of the graphs found have a so far unknown parameter set. Some examples generalize to an infinite family.</p>

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Some directed strongly regular graphs constructed from linear groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月4日

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  • Andries E. Brouwer,
  • Dean Crnković,
  • Andrea Švob,
  • Matea Zubović Žutolija

摘要

In this paper, we classify directed strongly regular graphs admitting a transitive action of one of the linear groups \(L_2(q), q\le 32\) , \(L_3(q), q \le 7\) , and \(L_4(2)\) , for which the rank of the permutation representation is at most 20. Several of the graphs found have a so far unknown parameter set. Some examples generalize to an infinite family.