Criticality of the lower domination parameters of graphs
Date
2007-03
Authors
Coetzer, Audrey
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
In this thesis we focus on the lower domination parameters of a graph G, denoted ¼(G), for
¼ 2 {i, ir, °}. For each of these parameters, we are interested in characterizing the structure of
graphs that are critical when faced with small changes such as vertex-removal, edge-addition and
edge-removal. While criticality with respect to independence and domination have been well
documented in the literature, many open questions still remain with regards to irredundance.
In this thesis we answer some of these questions.
First we describe the relationship between transitivity and criticality. This knowledge we then
use to determine under which conditions certain classes of graphs are critical. Each of the
chosen classes of graphs will provide specific examples of different types of criticality. We also
formulate necessary conditions for graphs to be ir-critical and ir-edge-critical.
Description
Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007.
Keywords
Irredundance, Independence, Criticality, Dissertations -- Applied mathematics, Theses -- Applied mathematics, Graphic methods, Domination (Graph theory)