Abstract

Following earlier work by Coons, Maraj, Misra and Sorea, and by Misra and Sullivant, we study colored, undirected Gaussian graphical models, and present a necessary and sufficient condition for such a model to have binomial vanishing ideal. These conditions involve Jordan schemes, a variant of association schemes, well-known structures in algebraic combinatorics. Using association schemes without transitive group action, we refute the conjecture by Coons, Maraj, Misra and Sorea that binomiality implies that the color classes must be orbits under the automorphism group of the colored graph.

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