Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2020
Committee Chair or Co-Chairs
Teresa Haynes, Rodney Keaton
Committee Members
Robert Gardner
Abstract
An Italian dominating function, abbreviated IDF, of $G$ is a function $f \colon V(G) \rightarrow \{0, 1, 2\}$ satisfying the condition that for every vertex $v \in V(G)$ with $f(v)=0$, we have $\sum_{u \in N(v)} f(u) \ge 2$. That is, either $v$ is adjacent to at least one vertex $u$ with $f(u) = 2$, or to at least two vertices $x$ and $y$ with $f(x) = f(y) = 1$. The Italian domination number, denoted $\gamma_I$(G), is the minimum weight of an IDF in $G$. In this thesis, we use operations that join two trees with a single edge in order to build trees with unique $\gamma_I$-functions.
Document Type
Thesis - unrestricted
Recommended Citation
England, Alyssa, "Trees with Unique Italian Dominating Functions of Minimum Weight" (2020). Electronic Theses and Dissertations. Paper 3741. https://dc.etsu.edu/etd/3741
Copyright
Copyright by the authors.