CSU Math 301
Fall 2015
Homework 12
Due Friday, December 4 at the beginning of class
Reading. Sections 9.2, 13.1, 13.2, 13.3
Remark. Make grammatically correct sentences by adding in just a few English words.
Problems.
1. Is the given code a valid Prüfer code? If so, draw the corresponding tree. If not,
explain why not (don’t just say “it doesn’t make a tree” — say how you could have
known in advance).
(a) 2585202
(b) 1139307
2. (a) Find a minimal spanning tree on the weighted graph drawn below. What is the
name of the algorithm you used?
(b) Draw a connected weighted graph that has at least two different minimal spanning
trees.
3. Let G be a connected weighted graph with positive edge costs.
(a) Describe how to find a spanning tree for which the sum of the edge-costs is maximal.
Hint: Create a new weighted graph G0 by multiplying the edge-costs of G by −1.
(b) Describe how to find a spanning tree for which the product of the edge-costs is
minimal.
Hint: Create a new weighted graph G0 by editing the edge-costs of G using logarithms.
4. Do Exercise 9.1.1 from the book. This exercise uses many of the same ingredients as
the proof that Kruskal’s algorithm works. Use Exercise 9.1.1 as an excuse to improve
your understanding of Kruskal’s algorithm.
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