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Chapter 4: Problem 3

Draw a graph that has more than one minimum spanning tree.

Short Answer

Expert verified
A graph with vertices A, B, C, D and having all equal edge weights can be created. In this case, more than one Minimum Spanning Tree (MST) can be formed.

Step by step solution

01

Draw Initial Graph

First, start by drawing a simple graph with some vertices. Let's say for instance that you have four vertices: A, B, C and D. Connect these vertices to form a simple square.
02

Assign Weights

Now assign the same weights to all edges of the graph. To create the edge weights all equal, you may assign every edge a weight of 2.
03

Review

Analyze and note that in this case more than one minimum spanning tree can be formed. For example, an MST can be obtained by taking the edges AB, AD and BD or BA, BC and AC.
04

Draw MSTs

Now, draw the minimum spanning trees. The first MST contains the edges AB, AD, BD and the second MST contains the edges BA, BC, AC.

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Most popular questions from this chapter

Use a greedy approach to write an algorithm for the Traveling Salesperson problem. Show that your algorithm does not always find a minimumlength tour.

Do you think it is possible for a minimum spanning tree to have a cycle? Justify your answer.

Assume that in a network of computers any two computers can be linked. Given a cost estimate for each possible link, should Algorithm 4.1 (Prim's algorithm) or Algorithm 4.2 (Kruskal's algorithm) be used? Justify your answer.

Can Dijkstra's algorithm (Algorithm 4.3) be used to find the shortest paths in a graph with some negative weights? Justify your answer.

Use Huffman's algorithm to construct an optimal binary prefix code for the letters in the following table. Letter \(: A B I M S \times Z\) Frequency : 1271810952
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