Fault-tolerance Research Of Locally Twisted Cubes And M((?)bius Cubes

In the study of interconnection network topology,graph theory has become a common method to construct interconnection network topology,and more and more scholars have applied graph theory to the study of interconnection network topology.In the measurement of fault-tolerant of network,pancyclicity and the path embedding have become a very important criteria,and has received extensive attentions from scholars.The reaserch of fault-tolerant of network is not only of great value in academic reaserch,but also is important in practical application.It can effectively improve and optimize the situation of a large network when unforeseen failures occur,so the large network still work when multiple lines and components fail simultaneously.Locally twisted cubes LTQn and Mobius cubes MQn are the variation of hypercube Qn.They are superior to hypercube Qn in fault-tolerant edge-pancyclicity and fault-tolerant hamiltonian-connected.Locally twisted cubes LTQn and Mobius cubes MQn have the same number of vertices as the hypercube Qn under the same dimension,but the diameter of Locally twisted cubes LTQn and Mobius cubes MQn are half of the hypercube Qn.In this paper,we studied the fault-tolerant edge-pancyclicity of LTQn and the fault-tolerant hamiltonian-connected of MQn by combining the method of computer search with mathematical induction.(1)Let F be a set of faulty elements in LTQn.If n?5 and |F|?n-2 then,for any fault-free edge e in LTQn-F and any integerl with 7?l?2n-fv,there is a fault-free l-cycle containing the edge e in LTQn-F.(2)MQn(n?5)is(n-2)-fault-tolerant Hamiltonian connected except(u,v)being a weak vertex-pair in MQn-F.