Abstract
Given a connected graph with the hitting time is defined as the expected number of steps that a simple random walk takes to go from x to y. A hitting-time-based invariant, called the ZZ index, was first proposed by Zhu and Zhang [The hitting time of random walk on unicyclic graphs. Linear Multilinear Algebra. doi:10.1080/03081087.2019.1611732] recently. It was defined to be In this paper, some extremal problems on the ZZ index of trees with some given parameters are considered. Firstly, sharp upper and lower bounds on are determined, respectively, for trees with given diameter, matching number, given vertex bipartition and given pendant numbers. Secondly, ordering the n-vertex caterpillar trees with respect to their ZZ indices are established.
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