Monotonic normalized heat diffusion for regular bipartite graphs with four eigenvalues

Abstract

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 eigenvalues, the ratio $H_t(u,v)/H_t(u,u),u,v\in V,$ is monotonically non-decreasing as a function of $t$. The key to the proof is the fact that such a graph is an incidence graph of a symmetric 2-design.

13 pages, 2 figures

References in corpus (1)

• On regular graphs with four distinct eigenvalues