The distinguishing number of a graph is the least number of colors in a vertex coloring such that the only color-preserving automorphism is trivial. The determining number of a graph is size of a smallest set of vertices $S$ such that the only automorphism fixing $S$ (point-wise) is trivial. I will discuss results on these symmetry parameters for Mycielskian graphs and for various types of cube graphs. This is joint work with Debra Boutin, Sally Cockburn, Lauren Keough, Kat Perry, and Puck Rombach.
Breaking Symmetries of Mycielskian Graphs and of Cubes
Sarah Loeb, Hampden-Sydney CollegeAuthors: Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, Kat Perry, Puck Rombach
2022 AWM Research Symposium
Women in Graph Theory and Applications