A set D of vertices in a graph G is a 2-dominating set of G if every vertex in V − D has at least two neighbors in D. The 2-domination number of a graph G, denoted by γ2(G), is the minimum cardinality of a 2- dominating set of G. In this thesis, we discuss the 2-domination number of a special family of trees, called caterpillars. A caterpillar is a graph denoted by Pk(x1, x2, ..., xk), where xi is the number of leaves attached to the ith vertex of the path Pk. First, we present the 2-domination number of some classes of caterpillars. Second, we consider several types of complete caterpillars. Finally, we consider classification of caterpillars with respect to their spine length and 2-domination number.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-4913 |
| Date | 01 August 2018 |
| Creators | Chukwukere, Presley |
| 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 0.0013 seconds