On Dense Triple-Loop Networks

Aguiló, Francesc; Simó, Ester; Zaragozá, Marisa

doi:10.1016/s1571-0653(04)00406-8

Cited by 2 publications

(3 citation statements)

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“…The dense family given by Aguiló, Simó, and Zaragozá [6] can be extended to a more general one. Using the same notation as in [6], take the integral matrix M (m, n) given by…”

Section: New Dense Familiesmentioning

confidence: 99%

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The Dilating Method for Cayley digraphs on finite Abelian groups

Aguiló¹,

Fiol²,

Pérez³

2016

Preprint

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A geometric method for obtaining an infinite family of Cayley digraphs of constant density on finite Abelian groups is presented. The method works for any given degree and it is based on consecutive dilates of a minimum distance diagram associated with a given initial Cayley digraph. The method is used to obtain infinite families of dense or asymptotically dense Cayley digraphs. In particular, for degree d = 3, an infinite family of maximum known density is proposed.

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“…The dense family given by Aguiló, Simó, and Zaragozá [6] can be extended to a more general one. Using the same notation as in [6], take the integral matrix M (m, n) given by…”

Section: New Dense Familiesmentioning

confidence: 99%

“…The diameter k = 7 is the minimum diameter a digraph Cay(Z 84 , {a, b, c}) can achieve. In [6,Proposition 3] it is stated that, for x ≡ 0 (mod 3), the digraph G M (2x+1,x) is isomorphic to a cyclic Cayley digraph and an explicit family is given. In the following result we extend this family to any value of x.…”

Section: Proposition 2 the Cayley Digraphmentioning

confidence: 99%

The Dilating Method for Cayley digraphs on finite Abelian groups

Aguiló¹,

Fiol²,

Pérez³

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…Notice that the fact N = αk d + O(k d−1 ) does not necessarily imply δ = α. For instance, a result of Dougherty and Faber [7,Corollary 8.2] gives the existence of cyclic Authors δ * Conditions on k Gómez, Gutiérrez & Ibeas [14] 0.0370 k ≡ 0, 1, 2 (mod 3) Aguiló, Fiol & García [3] 0.0740 k ≡ 2, 4, 5 (mod 6) Chen & Gu [6] 0.0780 No condition on k Aguiló [1] 0.0807 k = 22t + 12, t ≡ 2, 7 (mod 10) Aguiló, Simó & Zaragozá [4] 0.0840 k ≡ 2 (mod 30) As mentioned above, the concern of our paper are Cayley digraphs of Abelian groups. In this case, the bounds in (1) also apply for NA d,k .…”

Section: Introductionmentioning

confidence: 99%