On the hierarchical product of graphs

نویسندگان
Makar, Gabriela ID 1
Zajac, Piotr ID 2
Imrich, Wilfried ID 3
Palmen, Juliana ID 4

1 AGH University of Krakow, 30-059 Krakow, Poland

2 AGH University of Krakow, 30-059 Krakow, Poland

3 Montanuniversität Leoben, 8700 Leoben, Austria

4 AGH University of Krakow, 30-059 Krakow, Poland

doi
10.22061/jdma.2024.11171.1085
چکیده

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.

کلیدواژه‌ها
Hierarchical products of finite and infinite graphs, prime factor-izations, trees