Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2018
Committee Chair or Co-Chairs
Teresa Haynes
Committee Members
Robert A. Beeler, Anant Godbole
Abstract
Let $G$ be any graph and let $\overline{G}$ be its complement. The complementary prism of $G$ is formed from the disjoint union of a graph $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\overline{G}$. An Italian dominating function on a graph $G$ is a function such that $f \, : \, V \to \{ 0,1,2 \}$ and for each vertex $v \in V$ for which $f(v)=0$, it holds that $\sum_{u \in N(v)} f(u) \geq 2$. The weight of an Italian dominating function is the value $f(V)=\sum_{u \in V(G)}f(u)$. The minimum weight of all such functions on $G$ is called the Italian domination number. In this thesis we will study Italian domination in complementary prisms. First we will present an error found in one of the references. Then we will define the small values of the Italian domination in complementary prisms, find the value of the Italian domination number in specific families of graphs complementary prisms, and conclude with future problems.
Document Type
Thesis - unrestricted
Recommended Citation
Russell, Haley D., "Italian Domination in Complementary Prisms" (2018). Electronic Theses and Dissertations. Paper 3429. https://dc.etsu.edu/etd/3429
Copyright
Copyright by Haley D. Russell