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<p>For every odd prime power&#xa0;<i>q</i>, a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg group of order&#xa0;<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="373_2025_2941_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(q^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>q</mi> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> is constructed. It is proved that these digraphs are not distinguished by the Weisfeiler–Leman algorithm and have the Weisfeiler–Leman dimension&#xa0;3.</p>

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On a Family of Divisible Design Digraphs

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • M. Muzychuk,
  • G. Ryabov

摘要

For every odd prime power q, a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg group of order  \(q^3\) q 3 is constructed. It is proved that these digraphs are not distinguished by the Weisfeiler–Leman algorithm and have the Weisfeiler–Leman dimension 3.