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.
| Original language | English |
|---|---|
| Pages (from-to) | 163-171 |
| Number of pages | 9 |
| Journal | Journal of Discrete Mathematics and Its Applications |
| Volume | 9.2024 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 15 Sept 2024 |
Keywords
- Hierarchical products of finite and infinite graphs,
- prime factorizations
- trees