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In this paper, we study some operations which produce new divisor graphs from old ones. We prove that the contraction of a divisor graph along a bridge is a divisor graph. For two transmitters (receivers) u and v in some divisor orientation of a divisor graph G, it is shown that the merger G |u,v is also a divisor graph. Two special types of vertex… (More)

- Salah Al-Addasi, Omar A. AbuGhneim, Hassan Al-Ezeh
- Ars Comb.
- 2010

In this paper, we prove that for any positive integers k, n with k ≥ 2, the graph P k n is a divisor graph if and only if n ≤ 2k + 2, where P k n is the k power of the path Pn. For powers of cycles we show that C n is a divisor graph when n ≤ 2k + 2, but is not a divisor graph when n ≥ 2k + bk2 c+ 3, where C k n is the k th power of the cycle Cn. Moreover,… (More)

- Omar A. AbuGhneim, Hassan Al-Ezeh, Mahmoud Al-Ezeh
- Int. J. Math. Mathematical Sciences
- 2007

- Omar A. AbuGhneim, Ken W. Smith
- Electr. J. Comb.
- 2007

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 32and 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 the… (More)

- Omar A. AbuGhneim
- Ars Comb.
- 2016

This work examines the existence of (4q2,2q2 − q, q2 − q) difference sets, for q = p , where p is a prime and f is a positive integer. Suppose that G is a group of order 4q2 which has a normal subgroup K of order q such that G/K ∼= Cq × C2 × C2, where Cq,C2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or… (More)

- 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)

- Omar A. AbuGhneim
- Ars Comb.
- 2013

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