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Article Dans Une Revue Computers & Mathematics with Applications Année : 2011

A New Upper Bound for the (p,6) and the (p,8)-Cage

Alain Bretto
Alain Faisant
  • Fonction : Auteur
Luc Gillibert
  • Fonction : Auteur

Résumé

Constructing regular graphs with a given girth, a given degree and the fewest possible vertices is hard. This problem is called the cage graph problem and has some links with the error code theory. G-graphs can be used in many applications: symmetric and semi-symmetric graph constructions, (Bretto and Gillibert (2008) [12]), hamiltonicity of Cayley graphs, and so on. In this paper, we show that G-graphs can be a good tool to construct some upper bounds for the cage problem. For p odd prime we construct (p,6)-graphs which are G-graphs with orders 2p^2 and 2p^2-2, when the Sauer bound is equal to 4(p-1)^3. We construct also (p,8)-G-graphs with orders 2p^3 and 2p^3-2p, while the Sauer upper bound is equal to 4(p-1)^5.

Dates et versions

hal-01017290 , version 1 (02-07-2014)

Identifiants

Citer

Alain Bretto, Alain Faisant, Luc Gillibert. A New Upper Bound for the (p,6) and the (p,8)-Cage. Computers & Mathematics with Applications, 2011, 62 (6), pp.2472-2479. ⟨10.1016/j.camwa.2011.07.033⟩. ⟨hal-01017290⟩
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