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JMI2010A-9 Exact computation for the cover times of certain classes of trees (pp.93-98)

Author(s): Yusuke Higuchi, Takuya Ohwa and Tomoyuki Shirai

J. Math-for-Ind. 2A (2010) 93-98.

We show a special feature for the cover time of trees that is not satisfied by those of other graphs. By using this property, we show the relationship between the cover times of a tree and its subdivision, and we compute exactly the distribution of the last vertex visited by a random walk, the expectation and the Laplace transform of cover times of spider graphs as integral representations. We also discuss some comparison results for spider graphs.

Keyword(s).  cover time, first hitting time, terminal time, tree, subdivision, spider graph