Burning number of various graph families

Graph burning is a discrete process that models the transmission of a dominant idea within a community, also known as social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of contagion spread in a graph; the lower the burning number, the faster the spread. In this study, the burning numbers of certain graphs were examined, including path-forest graphs, Jahangir graphs, theta graphs, and cycle graphs with a single chord. Additionally, an algorithm was provided to calculate the burning number of path-forest graphs. Various results were obtained by examining graphs where certain vertices were already burned before the graph burning process started. Finally, different variations of graph burning were explored, and a new variation was introduced, along with the results obtained based on this variation.