Critical Pebbling Numbers of Graphs
Type of Work
Journal of Combinatorial Mathematics and Combinatorial Computing
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 2d.
Gibbons, Courtney R.; Laison, Joshua D.; and Paul, Erick J., "Critical Pebbling Numbers of Graphs" (2016). Hamilton Digital Commons.
Hamilton Areas of Study