Discrete Mathematics with Graph Theory (3rd Edition) 344

Discrete Mathematics with Graph Theory (3rd Edition) 344 -...

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342 Solutions to Exercises ~ A 2 ~ S B 1 2 2 E C 6 F (c) As shown on the right, the minimum weight of a spanning tree after T is removed is 18. The two least edges at T have weights 3 and 6, so we obtain 18 + 3 + 6 = 27 as a lower bound. (d) As shown to the right, if vertex C is removed, the minimum weight of a spanning tree is 26. The two least edges at C have weights 1 and 2 so we get an estimate of 26 + 1 + 2 = 29 as a lower bound. By way of comparison, the student should check that if vertex A is removed, the weight of a minimum spanning tree is 19, implying minimum Hamiltonian cycle of weight 8 A 2 ~3 S 3 T B E 6 F 19 + 2 + 6 = 27; if vertex D is removed, the weight of a minimum spanning tree is 23, implying minimum Hamiltonian cycle of weight 23 + 2 + 3 = 28; if vertex E is removed, the weight of a minimum spanning tree is 20, implying minimum Hamiltonian cycle of weight 20 + 2 + 3 = 25; if vertex F is removed, the weight of a minimum spanning tree is 15, implying minimum Hamiltonian cycle of weight 15
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