A new family of bridged and twisted hypercubes

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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