A. Porter

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math.CO2024

Eulerian $k$ -dominating reconfiguration graphs

M. E. Messinger, A. Porter

For a graph $G$ , the vertices of the $k$ -dominating graph, denoted $D_{k} (G)$ , correspond to the dominating sets of $G$ with cardinality at most $k$ . Two vertices of $\math…

math.CO2023

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…

math.CO2021

A note on hyperopic cops and robber

Nancy E. Clarke, Stephen Finbow, Margaret-Ellen Messinger +1

We explore a variant of the game of Cops and Robber introduced by Bonato et al.~where the robber is invisible unless outside the common neighbourhood of the cops. The hyperopic cop…

Eulerian k-dominating reconfiguration graphs

The damage number of the Cartesian product of graphs

A note on hyperopic cops and robber

Eulerian $k$ -dominating reconfiguration graphs