Changing the diameter of the locally twisted cube

The hypercube network Q n has been proved to be one of the most popular interconnection networks. The n-dimensional locally twisted cube LTQ n is an important variant of Q n . One of the critical performance factors of an interconnection network is the diameter which determines the maximum communication time between any pair of processors. In this paper, we investigate the diameter variability problems arising from the addition and deletion of edges in LTQ n . We obtain three results in this paper: (1) for any integer n≥2, we find the least number of edges (denoted by ch −(LTQ n )), whose deletion from LTQ n causes the diameter to increase, (2) for any integer n≥2, when ch −(LTQ n ) edges are deleted, the diameter will increase by 1 and (3) for any integer n≥4, the least number of edges whose addition to LTQ n will decrease the diameter is at most 2 n−1.

[1]  Frank Harary,et al.  Changing and Unchanging the Diameter of a Hypercube , 1992, Discret. Appl. Math..

[2]  Xie-Bin Chen,et al.  Paired many-to-many disjoint path covers of hypercubes with faulty edges , 2012, Inf. Process. Lett..

[3]  Sun-Yuan Hsieh,et al.  Edge-fault-tolerant hamiltonicity of locally twisted cubes under conditional edge faults , 2010, J. Comb. Optim..

[4]  Xiaofan Yang,et al.  Fault-tolerant embedding of meshes/tori in twisted cubes , 2011, Int. J. Comput. Math..

[5]  Gen-Huey Chen,et al.  Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs , 1999, IEEE Trans. Parallel Distributed Syst..

[6]  Chiun-Chieh Hsu,et al.  Independent spanning trees vs. edge-disjoint spanning trees in locally twisted cubes , 2010, Inf. Process. Lett..

[7]  Jun-Ming Xu,et al.  Panconnectivity of locally twisted cubes , 2006, Appl. Math. Lett..

[9]  David J. Evans,et al.  The locally twisted cubes , 2005, Int. J. Comput. Math..

[10]  Sun-Yuan Hsieh,et al.  Constructing edge-disjoint spanning trees in locally twisted cubes , 2009, Theor. Comput. Sci..

[11]  David J. Evans,et al.  Locally twisted cubes are 4-pancyclic , 2004, Appl. Math. Lett..

[12]  Guodong Zhou,et al.  Independent spanning trees on twisted cubes , 2012, J. Parallel Distributed Comput..

[13]  Jianxi Fan,et al.  Embedding meshes into locally twisted cubes , 2010, Inf. Sci..

[14]  Xin Liu,et al.  Efficient unicast in bijective connection networks with the restricted faulty node set , 2011, Inf. Sci..

[15]  Ting-Yi Sung,et al.  Diameter variability of cycles and tori , 2008, Inf. Sci..