Results regarding the pebbling number of various graphs are presented. We say a graph is of Class 0 if its pebbling number equals the number of its vertices. For diameter d we conjecture that everyâ€¦ (More)

We survey results on the pebbling numbers of graphs as well as their historical connection with a number-theoretic question of ErdÅ‘s and Lemke. We also present new results on two probabilisticâ€¦ (More)

A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of theâ€¦ (More)

Given a connected graph G, and a distribution of t pebbles to the vertices of G, a pebbling step consists of removing two pebbles from a vertex v and placing one pebble on a neighbor of v. For aâ€¦ (More)

The subject of graph pebbling has seen dramatic growth recently, both in the number of publications and in the breadth of variations and applications. Here we update the reader on the manyâ€¦ (More)

A Universal Cycle for t-multisets of [n] = {1, . . . , n} is a cyclic sequence of ( n+tâˆ’1 t ) integers from [n] with the property that each tmultiset of [n] appears exactly once consecutively in theâ€¦ (More)

A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. The pebbling number of a graph G is the minimumâ€¦ (More)

Let S be a cyclic n-ary sequence. We say that S is a universal cycle ((n, k)-Ucycle) for k-subsets of [n] if every such subset appears exactly once contiguously in S, and is a Ucycle packing if everyâ€¦ (More)