Monotonic normalized heat diffusion for distance-regular graphs with classical parameters of diameter 3

2025/05/07 by Liu, Shiping, Zhang, Heng
#Combinatorics (math.CO) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.04314

Abstract

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.

Citations

• Bounding the parameter β of a distance-regular graph with classical parameters
• An inequality for the heat kernel on an Abelian Cayley graph
• A Counterexample to Monotonicity of Relative Mass in Random Walks

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