Geodesic
Prime Factorization And Domination In The Hierarchical Product Of Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 4, pp. 873-890

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In 2009, Barrière, Dalfó, Fiol, and Mitjana introduced the generalized hierarchical product of graphs. This operation is a generalization of the Cartesian product of graphs. It is known that every connected graph has a unique prime factor decomposition with respect to the Cartesian product. We generalize this result to show that connected graphs indeed have a unique prime factor decomposition with respect to the generalized hierarchical product. We also give preliminary results on the domination number of generalized hierarchical products.
Keywords: generalized hierarchical product, Cartesian product, prime fac- tor decomposition 
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Anderson, S.E.; Guob, Y.; Tenney, A.; Wash, K.A. Prime Factorization And Domination In The Hierarchical Product Of Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 4, pp. 873-890. http://geodesic.mathdoc.fr/item/DMGT_2017_37_4_a2/