Construction
The hypercube graph Qn may be constructed using 2n vertices labeled 0,1,2,...,2n-1 and connecting two vertices whenever their Hamming distance equals 1. Additionally Qn+1 may be constructed using two hypercubes Qn and joining equivalent vertices together as shown in the above picture. The joining edges are called the (n+1)th dimension of Qn. Each dimension of Qn forms a perfect matching. Another definition of Qn is the Cartesian product of n two-vertex complete graphs K2.
Read more about this topic: Hypercube Graph
Famous quotes containing the word construction:
“When the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators; the instruments, not the guides, of the people.”
—Edmund Burke (1729–1797)
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“No construction stiff working overtime takes more stress and straining than we did just to stay high.”
—Gus Van Sant, U.S. screenwriter and director, and Dan Yost. Bob Hughes (Matt Dillon)