Solvability of Peg Solitaire on Octahedral Graph

Peg solitaire is a single-player board game that involves removing pegs from a board, usually leaving just one peg in the end. In the traditional game, jumps were only allowed to occur in a linear fashion. In this paper the jumps are allowed to occur in any direction since the layout of any graph in graph theory is arbitrary. In order to
completely solve board, or graph, these jumps must continue until only one peg remains. This Chapter obtains Peg Solitaire game is solvable, freely solvable on an octahedral graph. Deriving the result of playing Peg Solitaire on these graphs involve finding the optimal sequence of moves that allows to remove all but one peg from the graph, following the game rules. As the game proceeds the goal is to
minimize the number of pegs remaining on the board at the end. For derive the result of the game, strategies and logical thinking to plan the moves are required.