Average hitting times on Cartesian products of cycle powers and regular graphs decompose into a cycle component plus correction terms expressible as ratios of second-order linear recurrence sequences.
On walk-regular graphs and graphs with symmetric hitting times
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Aldous [1] asked whether every graph in which the distribution of the return time of random is independent of the starting vertex must be transitive. We remark that this question can be reduced into a purely graph-theoretic one that had already been answered Godsil & McKay [6] and ask some questions motivated by this.
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Average hitting times and recurrence structures II: Cartesian products of powers of cycles and regular graphs
Average hitting times on Cartesian products of cycle powers and regular graphs decompose into a cycle component plus correction terms expressible as ratios of second-order linear recurrence sequences.