A Note on the E-Optimality of Regular Line Graph Designs

Abstract

The recent work of Cameron (2009) on real symmetric matrices with zero diagonals, −1, 0, 1 entries, constant row sums, and the smallest eigenvalues greater than −2 provides a useful tool for studying E-optimal block designs. We use a result that restricts the possible values of the common row sum to show the E-optimality of some regular graph designs whose associated graphs are line graphs. In particular, L 2-type and triangular partially balanced incomplete block designs with λ2 = λ1 + 1 are shown to be E-optimal.