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.
Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-4976 |
Date | 01 December 2018 |
Creators | Gardner, Bradley |
Publisher | Digital Commons @ East Tennessee State University |
Source Sets | East Tennessee State University |
Language | English |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Electronic Theses and Dissertations |
Rights | Copyright by the authors. |
Page generated in 0.0018 seconds