# final(7) - CS 473G Final Exam Questions (May 5, 2007)...

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CS 473G Final Exam Questions (May 5, 2007) Spring 2007 You have 180 minutes to answer six of these questions. Write your answers in the separate answer booklet. 1. The d -dimensional hypercube is the graph deﬁned as follows. There are 2 d vertices, each labeled with a different string of d bits. Two vertices are joined by an edge if and only if their labels differ in exactly one bit. 00 10 11 0 1 01 000 100 010 110 001 101 011 111 The 1-dimensional, 2-dimensional, and 3-dimensional hypercubes. (a) [8 pts] Recall that a Hamiltonian cycle is a closed walk that visits each vertex in a graph exactly once. Prove that for all d 2 , the d -dimensional hypercube has a Hamiltonian cycle. (b) [2 pts] Recall that an Eulerian circuit is a closed walk that traverses each edge in a graph exactly once. Which hypercubes have an Eulerian circuit? [Hint: This is very easy.] 2. The University of Southern North Dakota at Hoople has hired you to write an algorithm to schedule their ﬁnal exams. Each semester, USNDH offers

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## This note was uploaded on 10/14/2011 for the course ECON 101 taught by Professor Smith during the Spring '11 term at West Virginia University Institute of Technology.

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final(7) - CS 473G Final Exam Questions (May 5, 2007)...

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