# Critical Pebbling Numbers of Graphs

@article{Gibbons2015CriticalPN, title={Critical Pebbling Numbers of Graphs}, author={Courtney R. Gibbons and Joshua D. Laison and Erick J. Paul}, journal={arXiv: Combinatorics}, year={2015} }

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… Expand

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