Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 11 - Section 11.5 - Minimum Spanning Trees - Exercises - Page 803: 17

Answer

Showing that there is a unique minimum spanning tree in a connected weighted graph if the weights of the edges are all different.

Work Step by Step

If all edges have different weights, - then a contradiction is obtained in the proof that Prim’s algorithm works when an edge ek+1 is added to T and an edge e is deleted, - instead of possibly producing another spanning tree.
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