Critical pebbling numbers of graphs


We define three new pebbling parameters of a connected graph $ G $, the $ r $-, $ g $-, and $ u $-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices $ n $ and the diameter $ d $ of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the $ r $-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the $ r $-critical pebbling number is $2^ d $.

Journal of Combinatorial Mathematics and Combinatorial Computing 99, 199-224