11 papers
Hypercups: Flipping Cups With More Than Two Sides
Micah Dykhuis, Lauren Keough, Sydney Lipton
In their 2010 article entitled ``How to invert cups at a time" in Mathematics Today, Man-Keung Siu and Ian Stewart extend a classic trick in which cups are flipped …
Symmetry Parameters of Various Hypercube Families
Debra Boutin, Sally Cockburn, Lauren Keough +2
In this paper we study the symmetry parameters determining number, distinguishing number, and cost of 2-distinguishing, for some variations on hypercubes, namely Hamming graphs, po…
Symmetry Parameters for Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
The Mycielskian construction, denoted , takes a finite simple graph to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielsk…
Determining Number and Cost of Generalized Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
A set of vertices is a determining set for a graph if every automorphism of is uniquely determined by its action on . The size of a smallest determining set for …
Distinguishing Generalized Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
A graph is -distinguishable if there is a coloring of the vertices with colors so that only the trivial automorphism preserves the color classes. The smallest such i…
An Extremal Problem for the Neighborhood Lights Out Game
Lauren Keough, Darren Parker
Neighborhood Lights Out is a game played on graphs. Begin with a graph and a vertex labeling of the graph from the set for . The game…