Prime factorization and domination in the hierarchical product of graphs | Zendy

Sarah E. Anderson | Zendy; Yaoqi Guo | Zendy; Asa Tenney | Zendy; Kirsti Wash | Zendy

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Prime factorization and domination in the hierarchical product of graphs

Author(s) -

Sarah E. Anderson,

Yaoqi Guo,

Asa Tenney,

Kirsti Wash

Publication year - 2017

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1952

Subject(s) - cartesian product , mathematics , prime factor , graph product , combinatorics , prime (order theory) , generalization , factorization , product (mathematics) , modular decomposition , graph , discrete mathematics , decomposition , chordal graph , pathwidth , 1 planar graph , line graph , algorithm , geometry , mathematical analysis , ecology , biology

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

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