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.

Author ORCID Identifier

https://orcid.org/0009-0001-7144-7120

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