Varieties of graphoids and Birkoff’s theorem for graphs - Bozapalidis, Symeon; Kalampakas, Antonios (Acta Cybernetica, 2017)
The algebraic structure of graphoids is used in order to obtain the wellknown Birkhoff’s theorem in the framework of graphs. Namely we establish a natural bijection between the class of Σ-graphoids and the class of strong congruences over GR(Σ, X), which is the free graphoid over the doubly ranked alphabet Σ and the set of variables X.