Some Properties Of The Cubelike Recursive Networks

Research of interconnection is an important aspect of mathematics and computer science research. It is widely used in graph theory, algorithm design and analyse, computer architecture, parallel and discrete computation, computer network and communication, and design of large scale integration circuit. The hypercube and its variations are a kind of interconnected networks model with better structure properties and network parameters, so it is favorite in research of interconnection.The dissertation discusses hypercube and its variations, and the main achievements are summarized as follows.(1) Proposing the concept of cubelike recursive interconnected function by analyzing existing hypercube and its variations (such as crossed cube, Mobius cube, generalized twisted cube, twisted n-cube and twisted cube networks), we conclude a kind of interconnected networks model which reflect the structure recursive property of hypercube and its variations and we name it cubelike recursive networks.(2) We analyze low-dimension topology, present an general algebra expression of cubelike recursive interconnected function. All of these works provide a new method of studying cubelike recursive networks.(3) We prove ^-dimension cubelike recursive networks are a kind of n regular network those connectivity is n. We discuss the problem of its diameter bound. We study its ability of fault-tolerance. We prove its wertex fault-tolerance and edge fault-tolerance are both n; ii. We present the border of its core; iii. We prove it is a 1-tenacious network; iv. We present the border of its discreteness;(4) We prove cubelike recursive networks are a kind of Hamiltonian graph. It is a constructed proof based on the structure recursive property of cubelike recursive networks. The method is skillful and the process is intuitionistic.