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Uniform equations for bipartite graphs and the center of a Terwilliger algebraŠtefko Miklavič,
Giusy Monzillo, 2026, original scientific article
Abstract: The uniform property was introduced by P. Terwilliger in the context of graded posets and was later extended to connected bipartite graphs. The core of this definition involves the so called uniform equations that must be satisfied. Let Γ denote a connected bipartite graph. Fix a vertex x of Γand let T=T(x) denote the corresponding Terwilliger algebra. In this paper, we study the connections between the uniform equations and the center of T. We show that these uniform equations give rise to a certain subspace of the center of T. Changing the logical direction, we show that if a matrix of a particular form belongs to the center of T, then uniform equations are satisfified.
Keywords: uniform equations, center of a Terwilliger algebra, bipartite graphs
Published in RUP: 08.05.2026; Views: 390; Downloads: 9
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