   Chapter 10.6, Problem 31ES ### 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 a connected, weighted graph G is input to Algorithm 10.6.4 (shown below), the output is a minimum spanning tree for G. Algorithm 10.6.4 Input: G (a connected graph] Algorithm Body: 1. T : = G . 2. E : = the set of all edges of G, m : = the number of edges of G. 3. while ( m > 0 ) 3a. Find an edge e in E that has maximal weight. 3b. Remove e from E and set m : = m − 1 . 3c. if the subgraph obtained when e is removed from the edge set of T is connected then remove e from the edge set of T end while Output: T [a minimum spanning tree for G]

To determine

To prove that if a connected, weighted graph G is the input given to following algorithm, the output will be minimum spanning tree for G.

Explanation

Given information:

The following is the given algorithm −

input: G[aconnectedgraph]Algorithm Body:1.T:=G2.E:=the set of all edges of G,m:=the number of edges of G.3.while(m>0)3a.Find an edgee from E that has maximal weight.3b.Removee fromE and set m:=m13c.ifthe subgraph obtained when e is removed from the edge set of Tis connected then removee fromthe edge set of T

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