Abstract
In 2011, Beeler and Hoilman introduced the game of peg solitaire to arbitrary graphs. It has been shown for several graph classes whether they are solvable or not. In this article, we give a new approach for considering peg solitaire on graphs, i.e., using pagoda functions. Pagoda functions are a classical tool for the original peg solitaire, but are, until now, almost never used for peg solitaire on graphs.In this article we develop some properties that pagoda functions on graphs need to satisfy. We also give an algorithm that constructs a pagoda function for an arbitrary graph (as long as this graph has a vertex of degree 1) and show how we can bound the peg solitaire number of certain graphs using this function.
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