The adjacency matrices and the transition matrices related to random walks on graphs

Abstract

A pointed graph $(\Gamma ,v_0)$ induces a family of transition matrices in Wildberger's construction of a hermitian hypergroup via a random walk on $\Gamma$ starting from $v_0$. We will give a necessary condition for producing a hermitian hypergroup as we assume a weaker condition than the distance-regularity for $(\Gamma ,v_0)$. The condition obtained in this paper connects the transition matrices and the adjacency matrices associated with $\Gamma$.

18 pages, 2 figures

References in corpus (1)

• Hypergroups and distance distributions of random walks on graphs