Monotonic normalized heat diffusion for regular bipartite graphs with four eigenvalues

Tasuku Kubo, Ryuya Namba

Let $X=(V,E)$ be a finite regular graph and $H_t(u,v),u,v\in V$, the heat kernel on $X$. We prove that, if the graph $X$ is bipartite and has four distinct Laplacian eigenv…