QuestionJuly 14, 2025

Identify the undirected graph represented by the adjacency matrix [} 0&1&3&0&4 1&2&1&3&0 3&1&1&0&1 0&3&0&0&2 4&0&1&2&3 ]

Identify the undirected graph represented by the adjacency matrix [} 0&1&3&0&4 1&2&1&3&0 3&1&1&0&1 0&3&0&0&2 4&0&1&2&3 ]
Identify the undirected graph represented by the adjacency matrix [} 0&1&3&0&4 1&2&1&3&0 3&1&1&0&1 0&3&0&0&2 4&0&1&2&3 ]

Solution
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Answer

The undirected graph has vertices {1, 2, 3, 4, 5} and edges with weights: (1,2), (1,3), (1,5), (2,3), (2,4), (3,5), (4,5). Explanation 1. Understand the adjacency matrix The given matrix represents weights between nodes. A zero indicates no direct connection. 2. Identify vertices and edges Vertices are numbered from 1 to 5. Non-zero entries indicate edges with weights. 3. List edges with weights From the matrix, extract edges: (1,2) with weight 1, (1,3) with weight 3, (1,5) with weight 4, (2,1) with weight 1, (2,2) with weight 2, (2,3) with weight 1, (2,4) with weight 3, (3,1) with weight 3, (3,2) with weight 1, (3,3) with weight 1, (3,5) with weight 1, (4,2) with weight 3, (4,5) with weight 2, (5,1) with weight 4, (5,3) with weight 1, (5,4) with weight 2, (5,5) with weight 3. 4. Construct the graph Use vertices and edges to draw the undirected graph.

Explanation

1. Understand the adjacency matrix<br /> The given matrix represents weights between nodes. A zero indicates no direct connection.<br />2. Identify vertices and edges<br /> Vertices are numbered from 1 to 5. Non-zero entries indicate edges with weights.<br />3. List edges with weights<br /> From the matrix, extract edges: (1,2) with weight 1, (1,3) with weight 3, (1,5) with weight 4, (2,1) with weight 1, (2,2) with weight 2, (2,3) with weight 1, (2,4) with weight 3, (3,1) with weight 3, (3,2) with weight 1, (3,3) with weight 1, (3,5) with weight 1, (4,2) with weight 3, (4,5) with weight 2, (5,1) with weight 4, (5,3) with weight 1, (5,4) with weight 2, (5,5) with weight 3.<br />4. Construct the graph<br /> Use vertices and edges to draw the undirected graph.
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