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<p>In a previous paper, the authors determined the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Hoffman coclique. As a counterpart of this result, in the present paper we determine the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Delsarte clique. In particular, an infinite family of strongly regular graphs with the required decomposition and a new infinite family of divisible design graphs are found.</p>

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Strongly regular graphs decomposable into a divisible design graph and a Delsarte clique

  • 期刊论文

  • 发表日期：

    2025年2月14日

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  • Alexander L. Gavrilyuk,
  • Vladislav V. Kabanov

摘要

In a previous paper, the authors determined the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Hoffman coclique. As a counterpart of this result, in the present paper we determine the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Delsarte clique. In particular, an infinite family of strongly regular graphs with the required decomposition and a new infinite family of divisible design graphs are found.