Abstract
The chapter reviews the Bose–Mesner algebra of a strongly regular graph Γ, and presents in the ith eigenspace Vi, i ∈ {1, 2} a special basis relative to some vertex of the graph. The Krein parameter is related to the components, with respect to the special basis, of a symmetric 3-tensor. The chapter also presents a definition of spherical i-designs in terms of tensors. The theorems explained in the chapter show that qiii = 0 if and only if Γ yields a spherical 3-design in Vi, and if and only if the sub-constituents of Γ yield spherical 2-designs in a hyperplane of Vi. The chapter presents a comparison of the restricted spectra of the sub-constituents of Γ. The chapter focuses on Smith graphs having (q + l) (q3 + 1) vertices, and on those having 16, 27, 100, 112, 162, and 275 vertices. Any graph of the first family is the point graph of a generalized quadrangle (q, q2).
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