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Use Prim's Algorithm starting at vertex SS to construct a minimum spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree?   a. {S,T}, {S,V}, {V,Z}, {W,Z}, {Y,Z}, {W,X}, {U,Y} b. {S,T}, {S,W}, {W,Z}, {V,Z}, {Y,Z}, {W,X}, {U,Y} c. {S,T}, {V,Z}, {W,Z}, {Y,Z}, {S,V}, {W,X}, {U,Y} d. {S,T}, {S,V}, {S,W}, {V,Z}, {W,X}, {Y,Z}, {U,Y}

Use Prim's Algorithm starting at vertex SS to construct a minimum spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree?   a. {S,T}, {S,V}, {V,Z}, {W,Z}, {Y,Z}, {W,X}, {U,Y} b. {S,T}, {S,W}, {W,Z}, {V,Z}, {Y,Z}, {W,X}, {U,Y} c. {S,T}, {V,Z}, {W,Z}, {Y,Z}, {S,V}, {W,X}, {U,Y} d. {S,T}, {S,V}, {S,W}, {V,Z}, {W,X}, {Y,Z}, {U,Y}

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
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Use Prim's Algorithm starting at vertex SS to construct a minimum spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree?

 

a. {S,T}, {S,V}, {V,Z}, {W,Z}, {Y,Z}, {W,X}, {U,Y}
b. {S,T}, {S,W}, {W,Z}, {V,Z}, {Y,Z}, {W,X}, {U,Y}
c. {S,T}, {V,Z}, {W,Z}, {Y,Z}, {S,V}, {W,X}, {U,Y}
d. {S,T}, {S,V}, {S,W}, {V,Z}, {W,X}, {Y,Z}, {U,Y}
### Graph Representation and Analysis The image is a weighted, undirected graph with nodes labeled \(S, T, U, V, W, X, Y,\) and \(Z\). The edges between these nodes have specific weights, which could represent distances, costs, or other metrics depending on context. Here's a detailed description of the graph: #### Nodes and Edges: - **Nodes** are depicted as circles and connected by lines, representing **edges**. - Each edge has a numerical **weight** associated with it, positioned near the middle of the line connecting two nodes. #### Connections with Weights: - \( S \) is connected to \( T \) with a weight of 2. - \( S \) is connected to \( W \) with a weight of 3. - \( S \) is connected to \( V \) with a weight of 3. - \( T \) is connected to \( X \) with a weight of 6. - \( U \) is connected to \( Y \) with a weight of 15. - \( V \) is connected to \( Z \) with a weight of 1. - \( W \) is connected to \( X \) with a weight of 4. - \( W \) is connected to \( Z \) with a weight of 2. - \( X \) is connected to \( Y \) with a weight of 4. - \( Y \) is connected to \( Z \) with a weight of 2. #### Graph Structure: The nodes are arranged in a structure forming a combination of paths and loops. Analyzing such a graph can help in understanding network connections, shortest paths between nodes, or other graph-related metrics and algorithms in graph theory or computer science education. This structured representation facilitates comprehension of network structures and can aid in teaching concepts such as network traversal, minimum spanning trees, or shortest path algorithms like Dijkstra's or Bellman-Ford.
Transcribed Image Text:### Graph Representation and Analysis The image is a weighted, undirected graph with nodes labeled \(S, T, U, V, W, X, Y,\) and \(Z\). The edges between these nodes have specific weights, which could represent distances, costs, or other metrics depending on context. Here's a detailed description of the graph: #### Nodes and Edges: - **Nodes** are depicted as circles and connected by lines, representing **edges**. - Each edge has a numerical **weight** associated with it, positioned near the middle of the line connecting two nodes. #### Connections with Weights: - \( S \) is connected to \( T \) with a weight of 2. - \( S \) is connected to \( W \) with a weight of 3. - \( S \) is connected to \( V \) with a weight of 3. - \( T \) is connected to \( X \) with a weight of 6. - \( U \) is connected to \( Y \) with a weight of 15. - \( V \) is connected to \( Z \) with a weight of 1. - \( W \) is connected to \( X \) with a weight of 4. - \( W \) is connected to \( Z \) with a weight of 2. - \( X \) is connected to \( Y \) with a weight of 4. - \( Y \) is connected to \( Z \) with a weight of 2. #### Graph Structure: The nodes are arranged in a structure forming a combination of paths and loops. Analyzing such a graph can help in understanding network connections, shortest paths between nodes, or other graph-related metrics and algorithms in graph theory or computer science education. This structured representation facilitates comprehension of network structures and can aid in teaching concepts such as network traversal, minimum spanning trees, or shortest path algorithms like Dijkstra's or Bellman-Ford.
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