Repository logo
 

On the integrity of domination in graphs.

dc.contributor.advisorSwart, Hendrika Cornelia Scott.
dc.contributor.authorSmithdorf, Vivienne.
dc.date.accessioned2012-11-30T13:34:08Z
dc.date.available2012-11-30T13:34:08Z
dc.date.created1993
dc.date.issued1993
dc.descriptionThesis (M.Sc.)-University of Natal, 1993.en
dc.description.abstractThis thesis deals with an investigation of the integrity of domination in a.graph, i.e., the extent to which domination properties of a graph are preserved if the graph is altered by the deletion of vertices or edges or by the insertion of new edges. A brief historical introduction and motivation are provided in Chapter 1. Chapter 2 deals with kedge-( domination-)critical graphs, i.e., graphsG such that )'(G) = k and )'(G+e) < k for all e E E(G). We explore fundamental properties of such graphs and their characterization for small values of k. Particular attention is devoted to 3-edge-critical graphs. In Chapter 3, the changes in domination number brought aboutby vertex removal are investigated. \ Parameters )'+'(G) (and "((G)), denoting the smallest number of vertices of G in a set 5 such that )'(G-5) > )'(G) ()'(G -5) < )'(G), respectively), are investigated, as are'k-vertex-critical graphs G (with )'(G) = k and )'(G-v) < k for all v E V(O)). The existence of smallest'domination-forcing sets of vertices of graphs is considered. The bondage number 'Y+'(G), i.e., the smallest number of edges of a graph G in a set F such that )'(G- F) > )'(0), is investigated in Chapter 4, as are associated extremal graphs. Graphs with dominating sets or domination numbers that are insensitive to the removal of an arbitrary edge are considered, with particular reference to such graphs of minimum size. Finally, in Chapter 5, we-discuss n-dominating setsD of a graph G (such that each vertex in G-D is adjacent to at least n vertices in D) and associated parameters. All chapters but the first and fourth contain a listing of unsolved problems and conjectures.en
dc.identifier.urihttp://hdl.handle.net/10413/8098
dc.language.isoen_ZAen
dc.subjectGraph theory.en
dc.subjectTheses--Mathematics.en
dc.titleOn the integrity of domination in graphs.en
dc.typeThesisen

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Smirthdorf_Vivienne_1993.pdf
Size:
10.51 MB
Format:
Adobe Portable Document Format
Description:
Thesis

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.64 KB
Format:
Item-specific license agreed upon to submission
Description: