Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge.

Author

Daniel Shelton Cantrell, East Tennessee State University

Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

5-2009

Committee Chair or Co-Chairs

Robert B. Gardner

Committee Members

Robert A. Beeler, Teresa W. Haynes

Abstract

In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:

(1) a single cycle of length v,

(2) f fixed points and a cycle of length v − f, or

(3) two disjoint cycles.

The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of K_v.

Document Type

Thesis - unrestricted

Recommended Citation

Cantrell, Daniel Shelton, "Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge." (2009). Electronic Theses and Dissertations. Paper 1872. https://dc.etsu.edu/etd/1872

Copyright

Copyright by the authors.