Improved Bounds for Burning Fence Graphs

Graph burning studies how fast a contagion, modeled as set of fires, spreads in graph. The process takes place synchronous, discrete rounds. In each round, fire breaks out at vertex, and the to all vertices that are adjacent vertex. number graph G is minimum rounds necessary for vertex burn. We consider \(m \times n\) Cartesian grid graphs, written \(G_{m,n}\). For = \omega (\sqrt{n})\), asymptotic value \(G_{m,n}\) was determined, but only growth rate investigated case O(\sqrt{n})\), which we refer fence graphs. provide new explicit bounds on graphs \(G_{c\sqrt{n},n}\), where \(c > 0\).