Consider a graph G, where each of the edges have different weights.Let T1 be the minimum-weight spanning tree produced by Kruskal's Algorithm, and let T2 be the minimum-weight spanning tree produced by Prim's Algorithm.I claim that T1 and T2 must be identical spanning trees - i.e., the exact same set of edges must appear in both trees.Determine whether this claim is TRUE or FALSE.If your answer is TRUE, see if you can figure out why the claim is true. If your answer is FALSE, see if you can come up with a counterexample.

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Answered: I claim that T1 and T2 must be…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Consider a graph G, where each of the edges have different weights.

Let T₁ be the minimum-weight spanning tree produced by Kruskal's Algorithm, and let T₂ be the minimum-weight spanning tree produced by Prim's Algorithm.

I claim that T₁ and T₂ must be identical spanning trees - i.e., the exact same set of edges must appear in both trees.

Determine whether this claim is TRUE or FALSE.

If your answer is TRUE, see if you can figure out why the claim is true. If your answer is FALSE, see if you can come up with a counterexample.

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