hypercube - CS 70 Fall 2006 Hypercubes Discrete Mathematics...

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CS 70 Discrete Mathematics for CS Fall 2006 Lecture 16 Hypercubes Recall that the set of all n -bit strings is denoted by { 0 , 1 } n . The n -dimensional hypercube is a graph whose vertex set is { 0 , 1 } n (i.e. there are exactly 2 n vertices, each labeled with a distinct n -bit string), and with an edge between vertices x and y iff x and y differ in exactly one bit position. i.e. if x = x 1 x 2 ... x n and y = y 1 y 2 ... y n , then there is an edge between x and y iff there is an i such that j n = i , x j = y j and x i n = y i . There is another equivalent recursive definition of the hypercube: The n -dimensional hypercube consists of two copies of the n - 1-dimensional hypercube (the 0-subcube and the 1-subcube), and with edges between corresponding vertices in the two subcubes. i.e. there is an edge between vertex x in the 0-subcube (also denoted as vertex 0 x ) and vertex x in the 1-subcube. Claim:
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This note was uploaded on 11/03/2008 for the course CMPSC 360 taught by Professor Haullgren during the Fall '08 term at Penn State.

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