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.
@article{bwmeta1.element.doi-10_7151_dmgt_1952,
author = {S.E. Anderson and Y. Guob and A. Tenney and K.A. Wash},
title = {Prime Factorization And Domination In The Hierarchical Product Of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {873-890},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1952}
}
S.E. Anderson; Y. Guob; A. Tenney; K.A. Wash. Prime Factorization And Domination In The Hierarchical Product Of Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 873-890. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1952/