Cyclic packing designs and simple cyclic leaves constructed from Skolem-type sequences

Alkasasbeh, Ahmad (2016) Cyclic packing designs and simple cyclic leaves constructed from Skolem-type sequences. Masters thesis, Memorial University of Newfoundland.

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Abstract

A Packing Design, or a PD(v; k; λ) is a pair (V; β) where V is a v-set of points and β is a set of k-subsets (blocks) such that any 2-subset of V appears in at most λ blocks. PD(v; k; λ) is cyclic if its automorphism group contains a v-cycle, and it is called a cyclic packing design. The edges in the multigraph λKᵥ not contained in the packing form the leaves of the CPD(v; k; λ); denoted by leave (v; k; λ) : In 2012, Silvesan and Shalaby used Skolem-type sequences to provide a complete proof for the existence of cyclic BIBD(v; 3; λ) for all admissible orders v and λ. In this thesis, we use Skolem-type sequences to find all cyclic packing designs with block size 3 for a cyclic BIBD(v; 3; λ) and find the spectrum of leaves graph of the cyclic packing designs, for all admissible orders v and λ with the optimal leaves, as well as determine the number of base blocks for every λ when k = 3.

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