摘要
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=Zm×H is a semiproduct of Zmby a subgroup H of G.In particular,if m is a prime,then the Cayley digraph of G has a hamiltonian circuit unless G=Zm×H.In addition,we introduce a new digraph operation,called φ-semiproduct of Γ1by Γ2and denoted by Γ1×Γ_φΓ2,in terms of mapping φ:V(Γ2)→{1,-1}.Furthermore we prove that C(Zm,{a})×_φ C(H,S) is also a Cayley digraph if φ is a homomorphism from H to{1,-1} ≤ Zm~*,which produces some classes of Cayley digraphs that have hamiltonian circuits.
基金
sponsored by the National Natural Science Foundation of China (No. 11671344)
Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2022D01A218)
the Scientific Research Projects of Universities in Xinjiang Province (No. XJEDU2019Y030)
