Date of Award
8-2024
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
Committee Chair/Advisor
Keri Ann Sather-Wagstaff
Committee Member
Michael Burr
Committee Member
Beth Novick
Abstract
Given a tree T and a field k, we define the open neighborhood ideal N(T) of T in k[V] to be the ideal generated by the open neighborhoods of all vertices in the graph. If T is unmixed with respect to the total domination problem, then it is known that N(T) is Cohen-Macaulay. Our goal is to compute the (Cohen-Macaulay) type of k[V]/N(T) using graph theoretical properties of T. We achieve this by using homological algebra and properties of monomial ideals. Along the way, we also provide a different characterization of unmixed trees and a generalization of the total dominating problem with the corresponding decomposition theorem.
Recommended Citation
Lim, Jounglag, "Cohen-Macaulay Type of Open Neighborhood Ideals of Unmixed Trees" (2024). All Theses. 4341.
https://open.clemson.edu/all_theses/4341
Author ORCID Identifier
0009-0005-7125-3624