Date of Award
5-2016
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Legacy Department
Mathematical Science
Committee Member
Dr. Kevin James, Committee Chair
Committee Member
Dr. Doug Rall
Committee Member
Dr. Wayne Goddard
Committee Member
Dr. Hui Xue
Abstract
The 'domination chain,'' first proved by Cockayne, Hedetniemi, and Miller in 1978, has been the focus of much research. In this work, we continue this study by considering unique realizations of its parameters. We first consider unique minimum dominating sets in Cartesian product graphs. Our attention then turns to unique minimum independent dominating sets in trees, and in some direct product graphs. Next, we consider an extremal graph theory problem and determine the maximum number of edges in a graph having a unique minimum independent dominating set or a unique minimum maximal irredundant set of cardinality two. Finally, we consider a variation of domination, called identifying codes, in the Cartesian product of a complete graph and a path.
Recommended Citation
Hedetniemi, Jason Todd, "Problems in Domination and Graph Products" (2016). All Dissertations. 1640.
https://open.clemson.edu/all_dissertations/1640