Hamiltonian cycle in the power graph of direct product two p-groups pf prime exponents

Author(s):

Alireza Doostabadi , Maysam Yaghoobian

Message:
Article Type:
Research/Original Article (بدون رتبه معتبر)
Abstract:

The power graph P(G) of a finite group G is a graph whose vertex set is the group G and distinct elements x; y are adjacent if one is a power of the other. Suppose that G = P * Q, where P (resp. Q) is a finite p-group (resp. q-group) of exponent p (resp. q) for distinct prime numbers p < q. In this paper, we determine necessary and sufficient conditions for existence of Hamiltonian cycles in P(G).

Keywords:

Power graph , Direct product , p-Group , Hamiltoniancycle

Language:
English
Published:
Caspian Journal of Mathematical Sciences, Volume:11 Issue: 1, Winter Spring 2022
Pages:
181 to 190
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