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I need to use Kruskal’s algorithm to find a minimum spanning tree T in the connected weighted graph and also show the order the edges are added to T. But, I'm completely lost

I need to use Kruskal’s algorithm to find a minimum spanning tree T in the connected weighted graph and also show the order the edges are added to T. But, I'm completely lost

Database System Concepts
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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I need to use Kruskal’s algorithm to find a minimum spanning tree T in the connected weighted graph and also show the order the edges are added to T. But, I'm completely lost

The image presents a weighted graph labeled \( G \). It consists of vertices and edges with assigned weights, forming a network. The graph includes the following vertices: \( p, q, r, s, t, u, v, w, x, y, \) and \( z \). Here's a breakdown of the graph's structure and weights: - **Vertices and Edges:** - Vertex \( p \) is connected to \( r \) (weight 9) and \( q \) (weight 7). - Vertex \( q \) is connected to \( s \) (weight 8) and \( t \) (weight 12). - Vertex \( r \) connects to \( v \) (weight 10). - Vertex \( s \) connects to \( v \) (weight 9) and \( w \) (weight 13). - Vertex \( t \) connects to \( w \) (weight 10) and \( z \) (weight 15). - Vertex \( u \) connects to \( r \) (weight 6), \( v \) (weight 10), and \( x \) (weight 11). - Vertex \( v \) connects to \( w \) (weight 14). - Vertex \( w \) connects to \( y \) (weight 8). - Vertex \( x \) connects to \( y \) (weight 5). - Vertex \( y \) connects to \( z \) (weight 7). - **Weights of Selected Edges:** - The edge \( (r, s) \) has a weight of 10. - The edge \( (v, w) \) has a weight of 14. - The edge \( (x, y) \) has a weight of 5. This graph can be used to study network optimization, shortest paths, or flow within networks, which are common topics in graph theory and discrete mathematics.
Transcribed Image Text:The image presents a weighted graph labeled \( G \). It consists of vertices and edges with assigned weights, forming a network. The graph includes the following vertices: \( p, q, r, s, t, u, v, w, x, y, \) and \( z \). Here's a breakdown of the graph's structure and weights: - **Vertices and Edges:** - Vertex \( p \) is connected to \( r \) (weight 9) and \( q \) (weight 7). - Vertex \( q \) is connected to \( s \) (weight 8) and \( t \) (weight 12). - Vertex \( r \) connects to \( v \) (weight 10). - Vertex \( s \) connects to \( v \) (weight 9) and \( w \) (weight 13). - Vertex \( t \) connects to \( w \) (weight 10) and \( z \) (weight 15). - Vertex \( u \) connects to \( r \) (weight 6), \( v \) (weight 10), and \( x \) (weight 11). - Vertex \( v \) connects to \( w \) (weight 14). - Vertex \( w \) connects to \( y \) (weight 8). - Vertex \( x \) connects to \( y \) (weight 5). - Vertex \( y \) connects to \( z \) (weight 7). - **Weights of Selected Edges:** - The edge \( (r, s) \) has a weight of 10. - The edge \( (v, w) \) has a weight of 14. - The edge \( (x, y) \) has a weight of 5. This graph can be used to study network optimization, shortest paths, or flow within networks, which are common topics in graph theory and discrete mathematics.
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