The access time of random walks on trees with given partition

Lihua Feng, Weijun Liu, Lu Lu, Wei Wang and Guihai Yu

Applied Mathematics and Computation, 2022, vol. 427, issue C

Abstract: Denote by T(s,t) the set of trees, whose vertex set can be partitioned into two independent sets of sizes s and t respectively. Given a tree T with stationary distribution π and a vertex v∈T, the access time HT(π,v) is the expected length of optimal stopping rules from π to v. In this paper, we get a sharp upper bound for maxv∈THT(π,v) and a sharp lower bound for minv∈THT(π,v) among T(s,t), respectively. The corresponding extremal graphs are also obtained. As a byproduct, it is proved that the path Pn maximizes maxv∈THT(π,v) and the star K1,n−1 minimizes minv∈THT(π,v) among all trees on n vertices.

Keywords: Tree; Random walk; Stopping rule (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002478

DOI: 10.1016/j.amc.2022.127173

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