A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
For a theoretical graph, the nth cube Q_n is a simple graph whose verices are the 2^n points (x_1...x_n) in R^n. So that for each x_i=0 or 1, and whose two vertices adjacent if thet agree in exactly n1 coordinates.
show that if n>=2 the Q_n has a hamiltonian cycle.
anonymous
 3 years ago
For a theoretical graph, the nth cube Q_n is a simple graph whose verices are the 2^n points (x_1...x_n) in R^n. So that for each x_i=0 or 1, and whose two vertices adjacent if thet agree in exactly n1 coordinates. show that if n>=2 the Q_n has a hamiltonian cycle.

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0• ok. so i am going to use induction and i hasve my base step be N=2 so i have a 2 dimensional cube with 2^2=4 vertives in R^2. with coordinates (00) (01) (10)(11)... which is really a two dimensional square with those coordinates as vertices. i can easily see it is a hamiltonian cycle.true.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i can even visualize a 3d cube whose eight vertices in R3whose edges are named: (000)(001)(010)(100)(011)(101)(110)(111) create a cube. which creates a hamiltonian cycyle. dw:1383750838900:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0however when i get to the n and n+1 i can't think of it... i don't know how to PROVE there is a hamiltonian cycle ... unless there is some formula that i can find to guarantee the edge numbers i need....
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.