Date of Award
5-2024
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
Committee Chair/Advisor
Wayne Goddard
Committee Member
Beth Novick
Committee Member
Svetlana Poznanovik
Abstract
We consider how the domination number of an undirected graph changes on the removal of a maximal matching. It is straightforward that there are graphs where no matching removal increases the domination number, and where some matching removal doubles the domination number. We show that in a nontrivial tree there is always a matching removal that increases the domination number; and if a graph has domination number at least $2$ there is always a maximal matching removal that does not double the domination number. We show that these results are sharp and discuss related questions.
Recommended Citation
Boyer, Geoffrey, "Domination in Graphs and the Removal of a Matching" (2024). All Theses. 4299.
https://tigerprints.clemson.edu/all_theses/4299
Author ORCID Identifier
https://orcid.org/0009-0001-7144-7120