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On Hamiltonian Property of Cayley Digraphs.
- Source :
- Acta Mathematicae Applicatae Sinica; Apr2024, Vol. 40 Issue 2, p547-556, 10p
- Publication Year :
- 2024
-
Abstract
- Let G be a finite group generated by S and C(G, S) the Cayley digraphs of G with connection set S. In this paper, we give some sufficient conditions for the existence of hamiltonian circuit in C(G, S), where G = Z<subscript>m</subscript> ⋊ H is a semiproduct of Z<subscript>m</subscript> by a subgroup H of G. In particular, if m is a prime, then the Cayley digraph of G has a hamiltonian circuit unless G = Z<subscript>m</subscript> × H. In addition, we introduce a new digraph operation, called φ-semiproduct of Γ<subscript>1</subscript> by Γ<subscript>2</subscript> and denoted by Γ<subscript>1</subscript> ⋊<subscript>φ</subscript> Γ<subscript>2</subscript>, in terms of mapping φ: V(Γ<subscript>2</subscript>) → {1, −1}. Furthermore we prove that C(Z<subscript>m</subscript>, {a}) ⋊<subscript>φ</subscript>C(H, S) is also a Cayley digraph if φ is a homomorphism from H to { 1 , − 1 } ≤ Z m ∗ , which produces some classes of Cayley digraphs that have hamiltonian circuits. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01689673
- Volume :
- 40
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Acta Mathematicae Applicatae Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 176299781
- Full Text :
- https://doi.org/10.1007/s10255-024-1023-9