Corpus ID: 18552580

Critical Pebbling Numbers of Graphs

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