Cohn–de Laat–Leijenhorst conjecture on maximal spherical codes from triangle-free strongly regular graphs

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Let GG be a connected triangle-free strongly regular graph (SRG) other than a complete bipartite graph. Let e2e_2 be the smallest eigenvalue of the adjacency matrix of GG, and let CC be the spherical code obtained by embedding GG into the eigenspace corresponding to e2e_2.

Cohn–de Laat–Leijenhorst conjecture. Three-point semidefinite programming bounds prove that CC is a maximal spherical code.

This conjecture proposes a broad application of semidefinite programming bounds to embeddings of triangle-free strongly regular graphs. The source attributes the conjecture to Cohn, de Laat, and Leijenhorst; its resolution is not specified here.

References

Primary source

P. G. Boyvalenkov, D. D. Cherkashin and P. D. Dragnev, “Universal optimality of T-avoiding spherical codes and designs”, arXiv:2501.13906 (2026).

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