Geoffrey Boyer

Assistant Professor

Education

Ph.D. in Mathematical Sciences, Clemson University

M.S. in Mathematical Sciences, Clemson University

B.S. in Mathematics, Wake Forest University

Research Interest

My primary research interests lie in several subareas of graph theory. In particular, I focus mostly on domination and domination related parameters of graphs. Dominating sets play an important role in graph theory and appear in many different settings. I have studied how the domination number changes on the removal of edges, and continue to study its recent generalization to what is now called isolation in graphs, which has caught the attention of many since its introduction ten years ago. The central questions of interest have been in computing upper bounds of various versions of the isolation number and determining the extremal graphs. Other than domination, I closely study measures of vulnerability of graphs. In particular, I have worked on the parameter toughness introduced by Chv´atal and considered extensively since. Lastly, I have started working in the field of generalizations of well-covered graphs. These are graphs where the greedy process always produces an optimal answer to a coloring problem.