39 Sectio Th I a 1 W a a a I N a Mor 0MN I a a 2 W 39 00 0 o 0 Q 1 o o 0 1 10 N 2 N 4 N 8 Figur The Nnode hypercube for N 2 4 and Two nodes are linked edge if and only if their i ID: 507849
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39 Sectio Th I a 1 W a a a I (N a Mor 0(M/N + I a a 2 W 3.1. Definitions and Properties 39 00 0 o 0 Q 1 \ o o 0 1 10 N 2 N 4 N 8 Figur The N-node hypercube for N = 2, 4, and Two nodes are linked edge if and only if their in precisely one bit position. Di 1 edges are shown in boldface. networ Th r-dimensional hypercube N = 2 a r = N 8 Th a dimension edge kth u uk u = u u kth kxth,, u. = a Th k a ak, 1 k N. k k 39 y-nod-nod ith ith 0 i I a (N/2). u = v = VyD? «i« N Viu � N »» N-lU\o Th A y y size, o weight, a (N/ N) I node edge (u, v) (u v') H, a H o~(u) = u' o(v) = v'. automorphism a a u = k (u, k' (u v'). n ,n(k') k, a 3.1. Definitions and Properties 39 Figur Construction of a four-dimensional hypercube (b) from two three-dimensional hypercubes Dashed a matching two three-dimensional cubes. 39 Figur Two labellings of the 8-node hypercube. By relabelling appropriately, we could have mapped edge e = to any position in the network. a(x =*(i ®u[) I " (aV(log/V © U\ogN)- (Her a a B.) a a A a(x (xi © I (x I I n) 3.1. On a a 4 x 4 a