TITLE

The Spectrum of Tetrahedral Quadruple Systems

AUTHOR(S)
Wang, Jian; Liang, Miao; Du, Beiliang
PUB. DATE
July 2011
SOURCE
Graphs & Combinatorics;Jul2011, Vol. 27 Issue 4, p593
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
n ordered analogue of quadruple systems is tetrahedral quadruple systems. A tetrahedral quadruple system of order v and index λ, TQS( v, λ), is a pair $${(S, \mathcal{T})}$$ where S is a finite set of v elements and $${\mathcal{T}}$$ is a family of oriented tetrahedrons of elements of S called blocks, such that every directed 3-cycle on S is contained in exactly λ blocks of $${\mathcal{T}}$$ . When λ = 1, the spectrum problem of TQS( v, 1) has been completely determined. It is proved that a TQS( v, λ) exists if and only if λ( v − 1)( v − 2) ≡ 0 (mod 3), λ v( v − 1)( v − 2) ≡ 0 (mod 4) and v ≥ 4.
ACCESSION #
61351958

 

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