A Study on Peg Solitaire and its Solvability

One of the most popular combinatorial puzzles under both
graph theory and recreational mathematics is "Peg Solitaire." The main idea of the game is to eliminate the pegs on the board by making a safe jump on the board. The game is associated with some challenging mathematical problems with regard to the transition of the configuration of the game. In this chapter, the game "Peg Solitaire"
is simulated by using the concept of graph theory, where the safe jumps are represented by paths of length two on the graph. The game can be extended to any graph structure, like paths, cycles, trees, and
multipartite graphs. The chapter introduces the concept of
solvability, covering the different forms of it, such as location solvability, strong solvability, and weak solvability, among others. Peg Solitaire, a game played on tripartite graphs, is discussed,highlighting the role of the structure of the graphs in the solvability of the game. Algorithmic approaches to the solution spaces,determining the solvability, are discussed, highlighting the role of
combinatorial and graph theory approaches to the study of a simple puzzle, giving a glimpse into the study of more complex problems in discrete mathematics.