Date of Award
5-2023
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
Deepak Bal
Committee Member
Jonathan Cutler
Committee Member
Ashwin Vaidya
Abstract
Given a graph G, we study the problem of finding a spanning tree T that maximizes the number of vertices of full degree; that is, the number of vertices whose degree in T equals its degree in G. We prove a few general bounds and then analyze this parameter on various classes of graphs including grid graphs, hypercubes, and random regular graphs. We also explore a related problem that focuses on maximizing the number of leaves in a spanning tree of a graph.
File Format
Recommended Citation
Acquaviva, Sarah, "The Full Degree Spanning Tree Problem" (2023). Theses, Dissertations and Culminating Projects. 1292.
https://digitalcommons.montclair.edu/etd/1292