Triangles and efficiency factors

Lindsay J Paterson; Peter Wild

doi:10.1093/biomet/73.2.289

Triangles and efficiency factors

Lindsay J Paterson
, Peter Wild

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We show that the number of triangles in the variety-concurrence graph of a regular-graph design can be used to derive upper bounds on the hatmonic-mean efficiency factor. The best alpha-lattice designs and the best cyclic designs have efficiency factors very close to the bounds. Our investigation gives insight into the structure of such designs. We see also that a certain type of regular-graph group-divisible design has a minimal number of triangles. © 1986 Biometrika Trust.

Original language	English
Pages (from-to)	289-299
Number of pages	11
Journal	Biometrika
Volume	73
Issue number	2
DOIs	https://doi.org/10.1093/biomet/73.2.289
Publication status	Published - Aug 1986

Keywords

Alpha-lattice design
Cyclic design
Incomplete block design
Upper bound on efficiency factor
Variety-concurrence graph

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10.1093/biomet/73.2.289

Cite this

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abstract = "We show that the number of triangles in the variety-concurrence graph of a regular-graph design can be used to derive upper bounds on the hatmonic-mean efficiency factor. The best alpha-lattice designs and the best cyclic designs have efficiency factors very close to the bounds. Our investigation gives insight into the structure of such designs. We see also that a certain type of regular-graph group-divisible design has a minimal number of triangles. {\textcopyright} 1986 Biometrika Trust.",

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AB - We show that the number of triangles in the variety-concurrence graph of a regular-graph design can be used to derive upper bounds on the hatmonic-mean efficiency factor. The best alpha-lattice designs and the best cyclic designs have efficiency factors very close to the bounds. Our investigation gives insight into the structure of such designs. We see also that a certain type of regular-graph group-divisible design has a minimal number of triangles. © 1986 Biometrika Trust.

KW - Alpha-lattice design

KW - Cyclic design

KW - Incomplete block design

KW - Upper bound on efficiency factor

KW - Variety-concurrence graph

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EP - 299

JO - Biometrika

JF - Biometrika

IS - 2

ER -

Triangles and efficiency factors

Abstract

Keywords

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