Date of Award

5-2024

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Jonathan Cutler

Committee Member

Deepak Bal

Committee Member

Ashwin Vaidya

Abstract

This thesis investigates various problems related to the number of strong dominating sets in a graph. Given a graph G, a set of vertices D is said to be dominating if every vertex outside of D has a neighbor in D. Bród and Skupién proved that the number of dominating sets in a tree T on n vertices is at most 2ⁿ⁻¹ + 1. A set S of vertices in a graph G is a strong dominating set if every vertex x outside of S has a neighbor y ∈ S with d(y) ≥ d(x). We investigate the number of strong dominating sets in paths and binary trees. We also give bounds on the number of strong dominating sets in regular graphs and trees.

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