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A New Family of Bridged and Twisted Hypercubes
October 1994 (vol. 43 no. 10)
pp. 1240-1247

We show that by adding eight extra edges, referred to as bridges, to an n-cube (n/spl ges/4) its diameter can be reduced by 2, and by adding sixteen bridges to an n-cube (n/spl ges/6) its diameter can be reduced by 3. We also show that by adding (/sub m+1sup 4m/)+1(m/spl ges/2) bridges to an n-cube (n/spl ges/4m and n/spl ges/8) its diameter can be reduced by 2m and by adding 2(/sub msup 4m-3/)+1, (m<2) to an n-cube (n/spl ges/4m-2 and n/spl ges/10) its diameter can be reduced by 2m-1. We also consider the reduction of diameter of an n-cube by exchanging some independent edges (twisting), where two edges are called independent if they are not incident on a common node. We have shown that by exchanging four pairs of independent edges in a d-cube (d/spl ges/5), we can reduce its diameter by 2. By exchanging sixteen pairs of independent edges, the diameter of a d-cube (d/spl ges/7) can be reduced by 3. By exchanging 57 pairs of independent edges, the diameter can be reduced by 4 for d/spl ges/9. To reduce the diameter by lower bound [d/2], (d/spl ges/10) we need to exchange (/sub r+1sup d-1/) pairs of independent edges, where r=lower bound [d/4]+1.

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Index Terms:
hypercube networks; hypercubes; bridged; routing; twisting; interconnection.
Citation:
R.K. Das, K. Mukhopadhyaya, B.P. Sinha, "A New Family of Bridged and Twisted Hypercubes," IEEE Transactions on Computers, vol. 43, no. 10, pp. 1240-1247, Oct. 1994, doi:10.1109/12.324555
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