Q17. Consider the graph with the following vertices, edges, and weights (weights are stated as the third entry for each edge in E, with the first two entries representing the vertices joined by the edge): V = {a, b, c, d, e, f, g} E = {{a, b, 10}, {a, c, 12}, {a, d, 15}, {a, f, 8}, {b, c, 11}, {b, e, 9}, {b, f, 3}, {c, d, 11}, {c, g, 14}, {d, e, 12}, {d, f, 10}, {f, g, 16}} b a C d e g What is the total weight of a minimum spanning tree of the graph?

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**Graph Description for Educational Website**

**Question 17:** Consider the graph with the following vertices, edges, and weights (weights are stated as the third entry for each edge in E, with the first two entries representing the vertices joined by the edge):

- **Vertices (V):** {a, b, c, d, e, f, g}

- **Edges (E):** 
  - {a, b, 10}
  - {a, c, 12}
  - {a, d, 15}
  - {a, f, 8}
  - {b, c, 11}
  - {b, e, 9}
  - {b, f, 3}
  - {c, d, 11}
  - {c, g, 14}
  - {d, e, 12}
  - {d, f, 10}
  - {f, g, 16}

**Graph Explanation:**

The graph consists of seven vertices labeled 'a' through 'g'. The edges connect these vertices and have associated weights indicated in the curly brackets. Each edge is represented by three values: two vertices and their connecting weight.

For example, the edge {a, b, 10} indicates a connection between vertices 'a' and 'b' with a weight of 10. The goal is to find the total weight of a minimum spanning tree (MST) for this graph.

**Diagram Description:**

The graph is displayed as a network of nodes (vertices) and connecting lines (edges) with specified weights. The vertices are evenly distributed, forming a connected and undirected graph.

**Exercise:**

- **Objective:** Determine the total weight of a minimum spanning tree of the graph.

Utilizing algorithms like Kruskal's or Prim's can help in identifying the MST by selecting the edges with minimal weights while ensuring all vertices remain connected with no cycles formed.
Transcribed Image Text:**Graph Description for Educational Website** **Question 17:** Consider the graph with the following vertices, edges, and weights (weights are stated as the third entry for each edge in E, with the first two entries representing the vertices joined by the edge): - **Vertices (V):** {a, b, c, d, e, f, g} - **Edges (E):** - {a, b, 10} - {a, c, 12} - {a, d, 15} - {a, f, 8} - {b, c, 11} - {b, e, 9} - {b, f, 3} - {c, d, 11} - {c, g, 14} - {d, e, 12} - {d, f, 10} - {f, g, 16} **Graph Explanation:** The graph consists of seven vertices labeled 'a' through 'g'. The edges connect these vertices and have associated weights indicated in the curly brackets. Each edge is represented by three values: two vertices and their connecting weight. For example, the edge {a, b, 10} indicates a connection between vertices 'a' and 'b' with a weight of 10. The goal is to find the total weight of a minimum spanning tree (MST) for this graph. **Diagram Description:** The graph is displayed as a network of nodes (vertices) and connecting lines (edges) with specified weights. The vertices are evenly distributed, forming a connected and undirected graph. **Exercise:** - **Objective:** Determine the total weight of a minimum spanning tree of the graph. Utilizing algorithms like Kruskal's or Prim's can help in identifying the MST by selecting the edges with minimal weights while ensuring all vertices remain connected with no cycles formed.
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