University of Isfahan Transactions on Combinatorics 2251-8657 13 3 2024 09 01 Peg solitaire on line graphs 257 277 27708 10.22108/toc.2023.131499.1935 EN Martin Kreh Institute of Mathematics and Applied Computer Science, University of Hildesheim, Samelsonplatz 1, 31141 Hildesheim, Germany 0000-0002-4302-6732 Jan-Hendrik De Wiljes Institute of Mathematics, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany 0000-0001-9854-648X Journal Article 2021 11 16 In $2011$, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. Since then peg solitaire and related games have been considered on many graph classes. One of the main goals is the characterization of solvable graphs. To this end, different graph operations, such as joins and Cartesian products, have been considered in the past. In this article, we continue this venue of research by investigating line graphs. Instead of playing peg solitaire on the line graph $L(G)$ of a graph $G$, we introduce a related game called stick solitaire and play it on $G$. This game is examined on several well-known graph classes, for example complete graphs and windmills. In particular, we prove that most of them are stick-solvable. We also present a family of graphs which contains unsolvable graphs in stick solitaire. Naturally, the Fool's stick solitaire number is an object of interest, which we compute for the previously considered graph classes. https://toc.ui.ac.ir/article_27708_c354e9e9d22ad44470c0d8ff3d2e9e95.pdf