4 research outputs found
Cyclic packing designs and simple cyclic leaves constructed from Skolem-type sequences
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