The 2-Domination Number of a Caterpillar

Author

Presley Chukwukere, East Tennessee State UniversityFollow

Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

8-2018

Committee Chair or Co-Chairs

Rodney Keaton

Committee Members

Robert A. Beeler, Teresa W. Haynes

Abstract

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 P_k(x₁, x₂, ..., x_k), where x_i is the number of leaves attached to the ith vertex of the path P_k. 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.

Document Type

Thesis - unrestricted

Recommended Citation

Chukwukere, Presley, "The 2-Domination Number of a Caterpillar" (2018). Electronic Theses and Dissertations. Paper 3456. https://dc.etsu.edu/etd/3456

Copyright

Copyright by the authors.