Date of Award
2014
Publisher
North Dakota State University
Document Type
Dissertation
Degree Awarded
Doctor of Philosophy (PhD)
Program
Mathematics
Department
Mathematics
College
Science and Mathematics
Faculty Advisor
Duncan, Benton
Description
In this dissertation, we explore various types of graphs that can be associated to a commutative ring with identity. In particular, if R is a commutative ring with identity, we consider a number of graphs with the vertex set being the set of proper ideals; various edge sets defined via different ideal theoretic conditions give visual insights and structure theorems pertaining to the multiplicative ideal theory of R. We characterize the interplay between the ideal theory and various properties of these graphs including diameter and connectivity.
Recommended Citation
Al-Kaseasbeh, Saba Zakariya, "Ideal Graphs" (2014). Mathematics. 18.
https://digitalcommons.ndsu.edu/mathematics/18
Rights
NDSU Policy 190.6.2
Rights Link
https://www.ndsu.edu/fileadmin/policy/190.pdf
Handle Identifier
https://hdl.handle.net/10365/27268