Geodesic
A prime factor theorem for a generalized direct product
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 135-140

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We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.
Keywords: products, set systems, prime factor theorem 
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Imrich, Wilfried; Stadler, Peter. A prime factor theorem for a generalized direct product. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 135-140. http://geodesic.mathdoc.fr/item/DMGT_2006_26_1_a11/