Cohn–de Laat–Leijenhorst conjecture on maximal spherical codes from triangle-free strongly regular graphs
Let be a connected triangle-free strongly regular graph (SRG) other than a complete bipartite graph. Let be the smallest eigenvalue of the adjacency matrix of , and let be the spherical code obtained by embedding into the eigenspace corresponding to .
Cohn–de Laat–Leijenhorst conjecture. Three-point semidefinite programming bounds prove that 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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