   Chapter 10.6, Problem 27ES ### 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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# Prove that if G is a connected, weighted graph and e is an edge of G that (1) has greater weight than any other edge of G and (2) is in a circuit of G, then there is no minimum spanning tree T for G such that e is in T.

To determine

To prove:

When G is a connected weighted graph and e is an edge of G which is in a circuit of G and that has larger weight than any other edge of graph G, then there exists no minimum spanning tree T for G such that the edge e is in T.

Explanation

Given information

G: Weighted graph

T1,T2: Distinct minimum spanning trees.

Concept used:

G' contains a nontrivial circuit.

Proof:

Suppose that there is a minimal spanning tree T for G such that e is in T.

Note that e is an edge of G and has larger weight than any other edge.

It is in a circuit of G.

Let P be another tree which has the same edges as in T except e

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