Discrete Mathematics with Graph Theory (3rd Edition) 327

Discrete Mathematics with Graph Theory (3rd Edition) 327 -...

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Section 12.1 5. [BB] S R1VOut S RTVOut S RTVOut S RTVOuI 6. Mary has six different ways to travel, avoiding the bus in four of these. Friday Saturday Plane Boat Plane Boat Plane Boat 7. [BB] There are (~) = 10 committees. ITDTDDTDDD A dh B rh 9. (a) The paths terminating at C are ABC, ABGFC, ABEFC, ADEBC, ADEBGFC, ADEFGBC, ADEFC, AEBC, AEBGFC, AEFC and AEFGBC. The Hamiltonian paths are ADEBCFG, ADEBGFC, ADEFGBC and ADEFCBG. (b) No Hamiltonian paths end at a vertex
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Unformatted text preview: adjacent to A so the graph is not Hamiltonian. (Alternatively, vertices C and G of degree 2 impose a proper circuit.) A B F D D Gee G 325 F G C B B C G (c) Since there are Hamiltonian paths from A, we seek a paving of roads which allows us to visit every town with paved roads from A. To do this at minimal cost, we should pave the roads along the Hamiltonian path ADEFCBG at a cost of 15. This path is the best of the Hamiltonian paths,...
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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.

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