No abstract

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 the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling number of a graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually put a pebble on every vertex simultaneously. We find the cover pebbling numbers of trees and some other graphs. We also consider the more general problem where (possibly different) given numbers of pebbles are required for the vertices.

In both Table 2 in the main article and Table 3 in the Instructor's Supplement of the original article, the number for the density functional calculation of energy for the enol form of acetylacetone should be -345.7998191 au, and the density functional calculation for the dipole moment of acetylacetone should be 2.98 D. The author regrets the error.