Monotonic normalized heat diffusion for distance-regular graphs with classical parameters of diameter $3$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908501610070016 |
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| author | Liu, Shiping Zhang, Heng |
| author_facet | Liu, Shiping Zhang, Heng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotonic normalized heat diffusion for distance-regular graphs with classical parameters of diameter $3$ Liu, Shiping Zhang, Heng Combinatorics Spectral Theory 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. |
| title | Monotonic normalized heat diffusion for distance-regular graphs with classical parameters of diameter $3$ |
| topic | Combinatorics Spectral Theory |
| url | https://arxiv.org/abs/2505.04314 |