  Recently, we initiated the study of random walk labelings of graphs. These
are graph labelings that are obtainable by performing a random walk on the
graph, such that each vertex is labeled upon its first visit. In this work, we
calculate the number of random walk labelings of several natural graph
families: The wheel, fan, barbell, lollipop, tadpole, friendship, and snake
graphs. Additionally, we prove several combinatorial identities that emerged
during the calculations.
