4 papers
On graph automorphisms related to Snort
Rylo Ashmore, Beth Ann Austin, Alfie M. Davies +2
We study the outcomes of various positions of the game Snort. When played on graphs admitting an automorphism of order two that maps vertices outside of their closed neighbourhoods…
Extremal Cat Herding
Rylo Ashmore, Danny Dyer, Rebecca Milley
The game of Cat Herding is one in which cat and herder players alternate turns, with the evasive cat moving along non-trivial paths between vertices, and the herder deleting single…
Deduction, Constrained Zero Forcing, and Constrained Searching
Andrea Burgess, Danny Dyer, Kerry Ojakian +3
Deduction is a recently introduced graph searching process in which searchers clear the vertex set of a graph with one move each, with each searcher's movement determined by which…
Graceful labellings of variable windmills using Skolem sequences
Ahmad H. Alkasasbeh, Danny Dyer, Jared Howell
In this paper, we introduce graceful and near graceful labellings of several families of windmills. In particular, we use Skolem-type sequences to prove (near) graceful labellings…