Two-Graphs

Authored by: Edward Spence

Handbook of Combinatorial Designs

Print publication date:  November  2006
Online publication date:  November  2006

Print ISBN: 9781584885061
eBook ISBN: 9781420010541
Adobe ISBN:

10.1201/9781420010541-112

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Abstract

13.1

A two-graph (V, Δ) consists of a set V whose elements are the vertices, and a collection Δ of unordered triples of the vertices (the odd triples), such that each 4-tuple of V contains, as subsets, an even number of elements of Δ. If (V, Δ) is a two-graph, then so also is the pair (V, V 3 \ Δ) the complement of (V, Δ).

A clique of a two-graph (V, Δ) is a subset C of V such that every triple from C is in Δ.

The two-graphs (V, Δ) and (V’, Δ’) are isomorphic if there is a bijection VV’ that induces a bijection Δ → Δ’.

The automorphism group Aut(V, Δ) of a two-graph (V, Δ) is the group of permutations of V that preserve Δ.

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