4 papers
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…