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.
Imrich, W., Makar, G., Palmen, J., & Zajac, P. (2024). On the hierarchical product of graphs. Journal of Discrete Mathematics and Its Applications, 9(3), 163-171. doi: 10.22061/jdma.2024.11171.1085
MLA
Wilfried Imrich; Gabriela Makar; Juliana Palmen; Piotr Zajac. "On the hierarchical product of graphs". Journal of Discrete Mathematics and Its Applications, 9, 3, 2024, 163-171. doi: 10.22061/jdma.2024.11171.1085
HARVARD
Imrich, W., Makar, G., Palmen, J., Zajac, P. (2024). 'On the hierarchical product of graphs', Journal of Discrete Mathematics and Its Applications, 9(3), pp. 163-171. doi: 10.22061/jdma.2024.11171.1085
VANCOUVER
Imrich, W., Makar, G., Palmen, J., Zajac, P. On the hierarchical product of graphs. Journal of Discrete Mathematics and Its Applications, 2024; 9(3): 163-171. doi: 10.22061/jdma.2024.11171.1085
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