4 papers · 1 filter
The damage number of the Cartesian product of graphs
Melissa A. Huggan, Margaret-Ellen Messinger, Amanda Porter
We consider a variation of Cops and Robber, introduced in [D. Cox and A. Sanaei, The damage number of a graph, [Aust. J. of Comb. 75(1) (2019) 1-16] where vertices visited by a rob…
Graph Burning On Large -Caterpillars
Danielle Cox, M. E. Messinger, Kerry Ojakian
Graph burning models the spread of information or contagion in a graph. At each time step, two events occur: neighbours of already burned vertices become burned, and a new vertex i…
The 2-burning number of a graph
C. B. Jacobs, M. E. Messinger, A. N. Trenk
We study a discrete-time model for the spread of information in a graph, motivated by the idea that people believe a story when they learn of it from two different origins. Similar…
Cops and Attacking Robbers with Cycle Constraints
Alexander Clow, Melissa A. Huggan, M. E. Messinger
This paper considers the Cops and Attacking Robbers game, a variant of Cops and Robbers, where the robber is empowered to attack a cop in the same way a cop can capture the robber.…