Double Jump Peg Solitaire on Graphs

Peg solitaire is a game in which pegs are placed in every hole but one and the player jumps over pegs along rows or columns to remove them. Usually, the goal is to have a single peg remaining. In a 2011 paper, this game is generalized to graphs. In this paper, we consider a variation in which each peg must be jumped twice in order to be removed. For this variation, we consider the solvability of several graph families. For our major results, we characterize solvable joins of graphs and show that the Cartesian product of solvable graphs is likewise solvable