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

2020/12/22 by Tomohiro Ikkai, Ikkai, Tomohiro, Hiromichi Ohno +3
Mathematics · #Finite Group Theory Research #Advanced Topics in Algebra #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2012.11880

Abstract

A pointed graph (Γ,v₀) induces a family of transition matrices in Wildberger's construction of a hermitian hypergroup via a random walk on Γ starting from v₀. We will give a necessary condition for producing a hermitian hypergroup as we assume a weaker condition than the distance-regularity for (Γ,v₀). The condition obtained in this paper connects the transition matrices and the adjacency matrices associated with Γ.

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