A dodecagon quadrangle is the graph consisting of two cycles: a 12-cycle (x1, x2,.., x12) and a 4-cycle (x1, x4, x7, x10). A dodecagon quadrangle system [DQS] of order v and index λ[DQSλ] is a pair Σ = (X; B), where X is a nite set of v vertices and B is a collection of edge disjoint dodecagon quadrangles (called blocks) which partitions the edge set of λKv, the complete multigraph with vertex set X. In [12] the authors determined the spectrum of DQSs having index λ = 1 and the spectrum of perfect DQSs in all the cases. In [14] we determine the spectrum of DQSs of index λ = 2n(2h + 1) > 1, for any h ∈ N and n = 0; 1; 2; 3. In this paper we complete the determination of the spectrum in all the remaining cases.

Dodecagon Quadrangle Systems having the most large spectrum

GIONFRIDDO, Mario;MARINO, LUCIA MARIA
2016

Abstract

A dodecagon quadrangle is the graph consisting of two cycles: a 12-cycle (x1, x2,.., x12) and a 4-cycle (x1, x4, x7, x10). A dodecagon quadrangle system [DQS] of order v and index λ[DQSλ] is a pair Σ = (X; B), where X is a nite set of v vertices and B is a collection of edge disjoint dodecagon quadrangles (called blocks) which partitions the edge set of λKv, the complete multigraph with vertex set X. In [12] the authors determined the spectrum of DQSs having index λ = 1 and the spectrum of perfect DQSs in all the cases. In [14] we determine the spectrum of DQSs of index λ = 2n(2h + 1) > 1, for any h ∈ N and n = 0; 1; 2; 3. In this paper we complete the determination of the spectrum in all the remaining cases.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/37928
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