Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24493220220901New heuristics for burning connected graphs165172491110.22060/ajmc.2022.21692.1101ENMaryamTahmasbiDepartment of Computer and Data Sciences, Shahid Beheshti University, Tehran, IranZahraRezai FarokhDepartment of Computer and Data Sciences, Shahid Beheshti University, Tehran, IranYousofBualiDepartment of Computer and Data Sciences, Shahid Beheshti University, Tehran, IranZahra Haj Rajab AliTehraniDepartment of Computer and Data Sciences, Shahid Beheshti University, Tehran, IranJournal Article20220820The concept of graph burning and burning number $(bn(G))$ of a graph $G$ was introduced recently [4]. Graph burning models the spread of contagion (fire) in a graph in discrete time steps. $bn(G)$ is the minimum time needed to burn a graph $G$. The problem is NP-complete. In this paper, we develop first heuristics to solve the problem in general (connected) graphs. In order to test the performance of our algorithms, we applied them on some graph classes with known burning number such as $\theta$-graphs. We tested our algorithms on DIMACS and BHOSLIB that are known benchmarks for NP-hard problems in graph theory. We also improved the upper bound for burning number on general graphs in terms of their distance to cluster. Then we generated a data set of 1000 random graphs with known distance to cluster and tested our heuristics on them.https://ajmc.aut.ac.ir/article_4911_62bb859d5f4ddd60bdd62f910c0da27d.pdf