# Prime Factorization And Domination In The Hierarchical Product Of Graphs

S.E. Anderson; Y. Guob; A. Tenney; K.A. Wash

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 4, page 873-890
- ISSN: 2083-5892

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topS.E. Anderson, et al. "Prime Factorization And Domination In The Hierarchical Product Of Graphs." Discussiones Mathematicae Graph Theory 37.4 (2017): 873-890. <http://eudml.org/doc/288388>.

@article{S2017,

abstract = {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.},

author = {S.E. Anderson, Y. Guob, A. Tenney, K.A. Wash},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {generalized hierarchical product; Cartesian product; prime fac- tor decomposition.},

language = {eng},

number = {4},

pages = {873-890},

title = {Prime Factorization And Domination In The Hierarchical Product Of Graphs},

url = {http://eudml.org/doc/288388},

volume = {37},

year = {2017},

}

TY - JOUR

AU - S.E. Anderson

AU - Y. Guob

AU - A. Tenney

AU - K.A. Wash

TI - Prime Factorization And Domination In The Hierarchical Product Of Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 4

SP - 873

EP - 890

AB - 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.

LA - eng

KW - generalized hierarchical product; Cartesian product; prime fac- tor decomposition.

UR - http://eudml.org/doc/288388

ER -

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