Question

Computer Science

Posted 5 months ago

```
What is the minimum possible weight of a spanning tree T
Group of choices:
1
8
1
3
2
6
2
1
1
7
```

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Answer from Sia

Posted 5 months ago

To determine the minimum possible weight of a spanning tree $T$ in a graph with 6 nodes and 9 edges, we can use Kruskal's algorithm or Prim's algorithm. Both algorithms are designed to find the Minimum Spanning Tree (MST) of a graph. Here, I'll use Kruskal's algorithm for simplicity.

```
- (1, 2) - 2
- (1, 4) - 1
- (1, 5) - 4
- (2, 3) - 3
- (2, 4) - 3
- (2, 6) - 7
- (3, 4) - 5
- (3, 6) - 8
- (4, 5) - 9
```

```
- Pick (1, 4) - 1
- Pick (1, 2) - 2
- Pick (2, 3) - 3
- Pick (2, 4) - 3 (forms a cycle, discard)
- Pick (1, 5) - 4
- Pick (3, 4) - 5 (forms a cycle, discard)
- Pick (2, 6) - 7
```

```
$1 + 2 + 3 + 4 + 7 = 17$
```

The minimum possible weight of a spanning tree $T$ is 17.

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