On the hierarchical product of graphs

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Imrich Wilfried; Makar Gabriela; Palmen Juliana; Zajac Piotr

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Journal Paper

Paper Information

Journal: Journal of Discrete Mathematics and its Applications Year:2024 | Volume:9 | Issue:3 Page(s): 163-171

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Information Journal Paper

Title

On the hierarchical product of graphs

Author(s)

Imrich Wilfried | Makar Gabriela | Palmen Juliana | Zajac Piotr | Issue Writer Certificate

Keywords

Hierarchical products of finite and infinite graphs

prime factor-izations

trees

Abstract

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.

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