PEBBLING IN DIAMETER 2 GRAPHS AND PRODUCTS OF PATHS

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 suf ficient connectivity is of Class 0. We verify the conjecture for d = 2 by characterizing those diameter two graphs of Class 0, extending res ults of Pachter, Snevily and Voxman. In fact we use this characterizat ion to show that almost all graphs have Class 0. We also present a tec hnical correction to Chung's alternate proof of a number theoretic res ult of Lemke and Kleitman via pebbling. (C) 1997 John Wiley & Sons, In c.