On the efficiency of regular generalized line graph designs

Abstract

A class of efficient designs called regular generalized line graph designs are introduced. This class of designs includes many well-known optimal and efficient designs, e.g., balanced incomplete block designs, group-divisible designs with λ 2 = λ 1 + 1, group-divisible designs with λ 1 = λ 2 + 1 and group size two, triangular designs with λ 2 = λ 1 + 1, L 2 designs with λ 2 = λ 1 + 1, etc. The optimality of regular generalized line graph designs is then investigated. This uses graph theory as a tool and unifies much of the previous work in the area.