The correct answer is: Graph M has 3 distinct minimum spanning trees, each of cost 2.

Here's why:

Step 1: Understand the adjacency matrix. The adjacency matrix M represents a graph with 3 vertices. The entries M[i][j] = 1 if there is an edge between vertices i and j, and M[i][j] = 0 if there is no edge. The diagonal entries are all 0, which means there are no loops in the graph.

Step 2: Understand the graph. The graph is a complete graph with 3 vertices, meaning that there is an edge between every pair of vertices.

Step 3: Understand the minimum spanning tree (MST). An MST of a graph is a subset of the edges that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

Step 4: Find the MSTs. In this case, since all the edges have the same weight (1), any tree that spans all the vertices will have the same total weight. There are 3 such trees: one that excludes the edge between vertices 1 and 2, one that excludes the edge between vertices 2 and 3, and one that excludes the edge between vertices 1 and 3.

Step 5: Check the options. The correct option is the one that says there are 3 distinct MSTs, each of cost 2. The cost is 2 because each MST has 2 edges, and each edge has weight 1.

Question

The correct answer is: Graph M has 3 distinct minimum spanning trees, each of cost 2.

Here's why:

Step 1: Understand the adjacency matrix. The adjacency matrix M represents a graph with 3 vertices. The entries M[i][j] = 1 if there is an edge between vertices i and j, and M[i][j] = 0 if there is no edge. The diagonal entries are all 0, which means there are no loops in the graph.

Step 2: Understand the graph. The graph is a complete graph with 3 vertices, meaning that there is an edge between every pair of vertices.

Step 3: Understand the minimum spanning tree (MST). An MST of a graph is a subset of the edges that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

Step 4: Find the MSTs. In this case, since all the edges have the same weight (1), any tree that spans all the vertices will have the same total weight. There are 3 such trees: one that excludes the edge between vertices 1 and 2, one that excludes the edge between vertices 2 and 3, and one that excludes the edge between vertices 1 and 3.

Step 5: Check the options. The correct option is the one that says there are 3 distinct MSTs, each of cost 2. The cost is 2 because each MST has 2 edges, and each edge has weight 1.

Knowee AI · Accepted Answer

The correct answer is: Graph M has 3 distinct minimum spanning trees, each of cost 2.

Here's why:

Step 1: Understand the adjacency matrix. The adjacency matrix M represents a graph with 3 vertices. The entries M[i][j] = 1 if there is an edge between vertices i and j, and M[i][j] = 0 if there is no edge. The diagonal entries are all 0, which means there are no loops in the graph.

Step 2: Understand the graph. The graph is a complete graph with 3 vertices, meaning that there is an edge between every pair of vertices.

Step 3: Understand the minimum spanning tree (MST). An MST of a graph is a subset of the edges that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

Step 4: Find the MSTs. In this case, since all the edges have the same weight (1), any tree that spans all the vertices will have the same total weight. There are 3 such trees: one that excludes the edge between vertices 1 and 2, one that excludes the edge between vertices 2 and 3, and one that excludes the edge between vertices 1 and 3.

Step 5: Check the options. The correct option is the one that says there are 3 distinct MSTs, each of cost 2. The cost is 2 because each MST has 2 edges, and each edge has weight 1.

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