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The Pi-Pebbling Function

T. Ballie Arnold
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Abstract

Recent research in graph pebbling has introduced the notion of a cover pebbling number. Along this same idea, we develop a more general pebbling function Pi(G, t, P). This measures the minimum number of pebbles needed to guarantee that any distribution of them on G can be transformed via pebbling moves to a distribution with pebbles on t target vertices. Furthermore, the P part of the function gives the ability to change how many pebbles are needed to pebble from one vertex to another. Bounds on the Pi-pebbling function are developed, as well as its exact value for several families of graphs.

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T. Ballie Arnold. 2005-06-22. The Pi-Pebbling Function. https://arxiv.org/abs/math/0506438

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