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<p>We prove the monotonic normalized heat diffusion property on distance-regular graphs with classical parameters of diameter 3. Regev and Shinkar found a Cayley graph for which this property fails. On the other hand, this property has been proved on abelian Cayley graphs, graphs with 3 distinct eigenvalues and regular bipartite graphs with 4 distinct eigenvalues by Price, Nica and Kubo-Namba, respectively. A distance regular graph with classical parameters of diameter 3 has 4 distinct eigenvalues and is not necessarily bipartite or vertex transitive.</p>

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Monotonic Normalized Heat Diffusion for Distance-Regular Graphs with Classical Parameters of Diameter 3

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Shiping Liu,
  • Heng Zhang

摘要

We prove the monotonic normalized heat diffusion property on distance-regular graphs with classical parameters of diameter 3. Regev and Shinkar found a Cayley graph for which this property fails. On the other hand, this property has been proved on abelian Cayley graphs, graphs with 3 distinct eigenvalues and regular bipartite graphs with 4 distinct eigenvalues by Price, Nica and Kubo-Namba, respectively. A distance regular graph with classical parameters of diameter 3 has 4 distinct eigenvalues and is not necessarily bipartite or vertex transitive.