For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?

The statement that is true for a given graph G having v vertices and e edges which is connected and has no cycles is: "The graph is a tree."

Here's why:

1. A graph is said to be connected if there is a path between every pair of vertices, which is given in the problem.

2. A graph is said to have no cycles if it does not contain any closed paths or loops, which is also given in the problem.

3. A tree is a type of graph that is connected and has no cycles.

4. Therefore, if a graph is connected and has no cycles, it is a tree.

5. Additionally, for a tree with v vertices, it will always have v-1 edges. This is known as the tree property. So, in this case, e should be equal to v-1.

So, the statement "The graph is a tree and it has v-1 edges" is true.