   Chapter 10.6, Problem 26ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# If G is a connected, weighted graph and no two edges of G have the same weight, does there exist a unique minimum spanning tree for G? Use the result of exercise 19 help justify your answer.

To determine

To check:

If G is a connected, weighted graph and no two edges of G have the same weight, then whether there exist a unique minimum spanning tree for G.

Explanation

Given information

G: Weighted graph

T1,T2: Distinct minimum spanning trees.

Concept used:

G' contains a nontrivial circuit.

Calculation:

At least one other edge f of this circuit is not in T1 and e is the edge of least weight that is in one of the trees and not the other. Remove f from G' to obtain a tree T3. Then, w(T3)<w(T2) because T3 is same as T2

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