Mathematics Commons^™

Cyclic, F-Cyclic, And Bicyclic Decompositions Of The Complete Graph Into The 4-Cycle With A Pendant Edge., Daniel Shelton Cantrell

Electronic Theses and Dissertations

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.

Decomposition, Packings And Coverings Of Complete Digraphs With A Transitive-Triple And A Pendant Arc., Janice Gail Lewenczuk

Electronic Theses and Dissertations

In the study of design theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K₃∪{e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings and coverings of the complete digraph with each of the six transitive triples with a pendant arc.