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- Title
Hamiltonian cycle in the power graph of direct product two p-groups of prime exponents.
- Authors
Doostabadi, Alireza; Yaghoobian, Maysam
- 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 ∈ G are adjacent if one is a power of the other, that is, x and y are adjacent if x ∈ ⟨y⟩ or y ∈ ⟨x⟩. 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).
- Subjects
HAMILTONIAN graph theory; PATHS &; cycles in graph theory; EXPONENTS; SET theory; GEOMETRIC vertices
- Publication
Caspian Journal of Mathematical Sciences, 2022, Vol 11, Issue 1, p181
- ISSN
2676-7260
- Publication type
Article