Hamiltonian properties of twisted hypercube-like networks with more faulty elements

Authors:
Xiaofan Yang;Qiang Dong;Erjie Yang;Jianqiu Cao
Affiliations:
College of Computer Science, Chongqing University, Chongqing 400044, China and School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, China;College of Computer Science, Chongqing University, Chongqing 400044, China and School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ...;College of Computer Science, Chongqing University, Chongqing 400044, China;School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, China
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

Twisted hypercube-like networks (THLNs) are a large class of network topologies, which subsume some well-known hypercube variants. This paper is concerned with the longest cycle in an n-dimensional (n-D) THLN with up to 2n-9 faulty elements. Let G be an n-D THLN, n=7. Let F be a subset of V(G)@?E(G), |F|@?2n-9. We prove that G-F contains a Hamiltonian cycle if @d(G-F)=2, and G-F contains a near Hamiltonian cycle if @d(G-F)@?1. Our work extends some previously known results.