On the hierarchical product of graphs
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In: Journal of Discrete Mathematics and Its Applications, Vol. 9.2024, No. 3, 15.09.2024, p. 163-171.
Research output: Contribution to journal › Article › Research › peer-review
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TY - JOUR
T1 - On the hierarchical product of graphs
AU - Imrich, Wilfried
AU - Makar, Gabriela
AU - Palmen, Juliana
AU - Zajac, Piotr
PY - 2024/9/15
Y1 - 2024/9/15
N2 - The hierarchical product of graphs is a variant of the Cartesian product. It is associative, not commutative, and finite connected graphs have unique first prime factors with respect to it. We present examples of infinite graphs with different first prime factors, and show that homogeneous trees of finite degree have unique prime factoriza-tions with respect to the hierarchical product. On the way, we pose two problems.
AB - The hierarchical product of graphs is a variant of the Cartesian product. It is associative, not commutative, and finite connected graphs have unique first prime factors with respect to it. We present examples of infinite graphs with different first prime factors, and show that homogeneous trees of finite degree have unique prime factoriza-tions with respect to the hierarchical product. On the way, we pose two problems.
KW - Hierarchical products of finite and infinite graphs,
KW - prime factorizations
KW - trees
UR - https://jdma.sru.ac.ir/article_2173_91c59a2519b519c562b6fd4c715cd22f.pdf
U2 - 10.22061/jdma.2024.11171.1085
DO - 10.22061/jdma.2024.11171.1085
M3 - Article
VL - 9.2024
SP - 163
EP - 171
JO - Journal of Discrete Mathematics and Its Applications
JF - Journal of Discrete Mathematics and Its Applications
SN - 2981-0809
IS - 3
ER -
