| Abstract: | 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 every graph of sufficient connectivity is of Class 0. We verify the conjecture for d = 2 by characterizing those diameter two graphs of Class 0, extending results of Pachter, Snevily and Voxman. In fact we use this characterization to show that almost all graphs have Class 0. We also present a technical correction to Chung's alternate proof of a number theoretic result of Lemke and Kleitman via pebbling. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 119–128, 1997 |
