Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 3

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

Short Answer

Expert verified
A square-shaped graph with all edges equal weight offers more than one minimum spanning tree. These MSTs are: MST 1 (edges AB, BC, CD) and MST 2 (edges BC, CD, DA), both having a total weight of 3 units.

Step by step solution

01

Create the Base Shape

Choose an identifiable shape that has more than one route from one point to another. A square or rectangle serves as the best example here. Draw in a square shape with four vertices named, for instance, A, B, C, D, with AB, BC, CD and DA as edges. Ensure all edges have equal weights, e.g., all having a weight of 1.
02

Identify Possible Minimum Spanning Trees

A minimum spanning tree is a subgraph that spans all the vertices in a graph while having the minimal total edge weight possible. Advocating the equal edge weights in our square, there are 2 possible MSTs: MST 1 includes edges AB, BC, CD. MST 2 includes edges BC, CD, DA. Both MSTs cover all vertices (A, B, C, D) and have same total weight (3 units).
03

Depict Minimum Spanning Trees

For visual understanding, draw the two MSTs independently, showing the graph in a different color or style to differentiate the minimum spanning trees from the complete graph.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Implement Prim's Algorithm (Algorithm 4,1) on your system, and study its performance using different graphs.

Implement Kruskal's Algorithm (Algorithm 4.2) on your system, and study its performance using different graphs

Use a greedy approach to construct an optimal binary search tree by considering the most probable key, \(K e y_{2}\), for the root, and constructing the left and right subtrees for \(K e y_{1}, K e y_{2}, \ldots, K e y_{2}-1,\) and \(K e y_{2}+\ldots, K e y_{2}+2 \ldots \ldots, K e y_{2}\) recursively in the same way. (a) Assuming the keys are already sorted, what is the worst-case time complexity of this approach? Justify your answer. (b) Use an example to show that this greedy approach does not always find an optimal binary search tree.

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

Use a greedy approach to write an algorithm for the Traveling Salesperson Problem. Show that your algorithm does not always find a minimum-length tour.
See all solutions

Recommended explanations on Computer Science Textbooks

Theory of Computation

Read Explanation

Computer Network

Read Explanation

Big Data

Read Explanation

Algorithms in Computer Science

Read Explanation

Game Design in Computer Science

Read Explanation

Problem Solving Techniques

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free