6 papers
Discrete-time treatment number of binary trees
Karen L. Collins, Margaret-Ellen Messinger, Ann N. Trenk
The discrete-time treatment number of a graph , denoted by , was introduced in arXiv:2408.0531(3) and arises from a deterministic process in which each vertex is assigned…
On Pancyclicity in a Mixed Model for Domination Reconfiguration
Margaret-Ellen Messinger, Logan Pipes
A new model for domination reconfiguration is introduced which combines the properties of the preexisting token addition/removal (TAR) and token sliding (TS) models. The vertices o…
Discrete-time treatment number
N. E. Clarke, K. L. Collins, M. E. Messinger +2
We introduce the discrete-time treatment number of a graph, in which each vertex is in exactly one of three states at any given time-step: compromised, vulnerable, or treated. Our…
Eulerian -dominating reconfiguration graphs
M. E. Messinger, A. Porter
For a graph , the vertices of the -dominating graph, denoted , correspond to the dominating sets of with cardinality at most . Two vertices of $\math…
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…