Discrete Mathematics with Graph Theory (3rd Edition) 339

Discrete Mathematics with Graph Theory (3rd Edition) 339 -...

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Unformatted text preview: Section 12.3 337 5. (a) (b) iv. Choose DE, AC, AB, AG and AE in order. There are two possibilities for an edge of weight 4. We choose AF, obtaining the spanning tree on the right, of maximal weight 39. v. Choose IG, IH, CD, DM, AB, BJ, GF, I A and J L. At this point, the next edge of highest weight, H G, cannot be selected since it would complete a circuit with previously chosen edges. So choose BC and CK. We are not able to choose KM or GL, so we select FE, giving a spanning tree of maximum weight 89. I C E F Start with any vertex and the edge of maximum weight incident with that vertex. Then pick an edge of maximum weight from among those edges adjacent to the first. In general, given a subgraph of the given graph which is a tree but not a spanning tree, add to this an edge of maximum weight from those edges one of whose end vertices is not in the tree and the other of which is (so that the augmented tree is also a tree). Continue until there are no vertices outside the tree, that is, until augmented tree is also a tree)....
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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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