Random Walk Labelings of Perfect Trees and Other Graphs

A Random walk labeling of a graph $G$ is any labeling of $G$ that could have been obtained by performing a random walk on $G$. Continuing two recent works, we calculate the number of random walk labelings of perfect trees, combs, and double combs, the torus $C_2\times C_n$, and the graph obtained by connecting three path graphs to form two cycles.