The correct answer is (b) v = e + 1.

Here's why:

A graph G that is connected and has no cycles is a tree. One of the properties of a tree in graph theory is that it has one less edge than it has vertices. This is because every vertex (except the root) must be connected to exactly one other vertex, thus creating an edge.

So, if you have v vertices, you will have v - 1 edges. But the question states that the graph has e edges. Therefore, we can say that e = v - 1.

If we rearrange this equation to solve for v, we get v = e + 1.

So, the correct answer is (b) v = e + 1.

Question

The correct answer is (b) v = e + 1.

Here's why:

A graph G that is connected and has no cycles is a tree. One of the properties of a tree in graph theory is that it has one less edge than it has vertices. This is because every vertex (except the root) must be connected to exactly one other vertex, thus creating an edge.

So, if you have v vertices, you will have v - 1 edges. But the question states that the graph has e edges. Therefore, we can say that e = v - 1.

If we rearrange this equation to solve for v, we get v = e + 1.

So, the correct answer is (b) v = e + 1.

Knowee AI · Accepted Answer

The correct answer is (b) v = e + 1.

Here's why:

A graph G that is connected and has no cycles is a tree. One of the properties of a tree in graph theory is that it has one less edge than it has vertices. This is because every vertex (except the root) must be connected to exactly one other vertex, thus creating an edge.

So, if you have v vertices, you will have v - 1 edges. But the question states that the graph has e edges. Therefore, we can say that e = v - 1.

If we rearrange this equation to solve for v, we get v = e + 1.

So, the correct answer is (b) v = e + 1.

For a given graph G having v vertices and e edges which is connected and has nocycles, which of the following statements is true?(a) v = e(b) v = e + 1(c) v + 1 = e(d) v = e – 1

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