Define the hypercube Qn as follows. The vertex set of Qn is the collection of all 01-strings of length n. Two vertices are joined by an edge if and only if they differ in exactly one bit. Determine the number of vertices, edges and degrees in Q,. Show that Qn is connected.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 74EQ
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Define the hypercube Qn as follows. The vertex set of Qn is the collection of all 01-strings of length n. Two vertices are joined by an edge if and only if they differ in exactly one bit. Determine the number of vertices, edges and degrees in Qn. Show that Qn is connected.

Define the hypercube Qn as follows. The vertex set of Qn is the collection of all
01-strings of length n. Two vertices are joined by an edge if and only if they differ
in exactly one bit. Determine the number of vertices, edges and degrees in Qn. Show
that Qn is connected.
Transcribed Image Text:Define the hypercube Qn as follows. The vertex set of Qn is the collection of all 01-strings of length n. Two vertices are joined by an edge if and only if they differ in exactly one bit. Determine the number of vertices, edges and degrees in Qn. Show that Qn is connected.
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