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Unformatted text preview: A B ~ degree two, both edges incident with them would be on a Hamiltonian {:} cycle, but this forms a smaller cycle not containing all vertices, that is, a A B proper cycle. (d) [BB] ~ 1 2 7 3 6 4 5 (e) This is not Hamiltonian. Since the vertices labeled A, B, C and D are of degree two, both edges incident with each of them would be on a Hamiltonian cycle, but these eight edges would then form a proper cycle, as shown. A B m D C (t) This is a pseudograph, but not a graph, so the question does not apply. The definitions of Section 10.2 were given only for graphs. 3. (a) (b) 18 1 9 4 2 3 5 8 6 7 (a) The graph in (a) is Hamiltonian; a Hamiltonian cycle is indicated. Any Hamiltonian graph has a Hamiltonian path....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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