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Abstract: In graph pegging, we view each vertex of a graph as a hole into which a pegcan be placed, with checker-like ``pegging moves- allowed. Motivated bywell-studied questions in graph pebbling, we introduce two pegging quantities.The pegging number respectively, the optimal pegging number of a graph is theminimum number of pegs such that for every respectively, some distribution ofthat many pegs on the graph, any vertex can be reached by a sequence of peggingmoves. We prove several basic properties of pegging and analyze the peggingnumber and optimal pegging number of several classes of graphs, includingpaths, cycles, products with complete graphs, hypercubes, and graphs of smalldiameter.



Autor: Geir Helleloid, Madeeha Khalid, David Petrie Moulton, Philip Matchett Wood

Fuente: https://arxiv.org/







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