Discrete Mathematics with Graph Theory (3rd Edition) 360

# Discrete Mathematics with Graph Theory (3rd Edition) 360 -...

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358 Solutions to Review Exercises 11. First select edges AD, BE, CF, GJ and I J of weight 1. Then select edges AB, CG, I K of weight 2. Since G1 would complete a circuit, we cannot select this edge. Since J K and FG would also complete circuits, we cannot select these either. We select next CE of weight 5. Since BC and EF would complete circuits, we cannot select them, so we next select HI or H K of weight 7. We now have 10 edges, the necessary number for a spanning tree, so we are done. The weight of our tree is 5 + 6 + 5 + 7 = 23. 12. Let us start at vertex A. We first select AD, then AB. Next BE is selected and following that comes EC. Then come CF and CG. Next we select GJ and then J1. Then comes 1K and finally 1H. The tree obtained by Prim is the same as that obtained by Kruskal in Exercise 11. 13. We use Kruskal's algorithm. The edge of least weight is VI V2, of weight 3 and the next edge chosen is VI v3, of weight 4. There are two edges of weight 5, VI V4 and V2V3, but V2V3 will complete a circuit. We choose VI V4. The process continues: if VI V2, ... ,
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