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In this paper, we prove that for any positive integers k, n with k ≥ 2, the graph P

- Omar A. AbuGhneim, Hasan A. Al-Halees, Ahmed M. Assaf
- 2009

A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are regarded as ordered k-tuples and in which each ordered pair of elements occurs in at least λ blocks. Let DE(v, k, λ) denote the minimum number of blocks in a DC(v, k, λ). In this paper the values of the function DE(v, k, λ) are determined for all odd integers v… (More)

We resolve the existence problem of (96, 20, 4) difference sets in 211 of 231 groups of order 96. If G is a group of order 96 with normal subgroups of orders 3 and 4 then by first computing 32-and 24-factor images of a hypothetical (96, 20, 4) difference set in G we are able to either construct a difference set or show a difference set does not exist. Of… (More)

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