Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
12-2018
Committee Chair or Co-Chairs
Teresa Haynes
Committee Members
Robert A. Beeler, Frederick Norwood
Abstract
An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination number for ladders, specific families of prisms, mobius ladders and related products including categorical products $G\times K_2$ and lexicographic products $G\cdot K_2$. Finally, we will conclude with open problems.
Document Type
Thesis - unrestricted
Recommended Citation
Gardner, Bradley, "Italian Domination on Ladders and Related Products" (2018). Electronic Theses and Dissertations. Paper 3509. https://dc.etsu.edu/etd/3509
Copyright
Copyright by the authors.