Research and Exposition in Mathematics -- Volume 3
Connectivity in Multi-Factor Designs.
A Combinatorial Approach
200 p., soft cover, ISBN 3-88538-203-2, EUR 10.00, 1982
Designs have to be connected so that contrasts between factor levels can be estimated. This
monograph presents useful new characterizations of connectivity, derived through graph theory.
It has substantial results to offer on designs for three or more factors and in particular on
row-and-column designs. The most useful of these constitute an algorithmic approach to checking
whether a design is connected. The algorithm is based on an easily defined digraph, and the
maximum number of independent cycles in this graph. The algorithm works economically because
complicated digraphs can be reduced by straightforward rules to elementary digraphs without
altering the maximum number of independent cycles.
"I found the book extremely interesting and stimulating and was motivated to write a paper
on the subject. I can recommend the book to anyone with an interest in the theory of
(J. Opl. Res. Soc.)
"Its new techniques for investigating connectivity are a valuable addition to statistical
kowledge, and it should be on the bookshelves of all those whose research interests include
(Australian J. Statistics)