It is a connected, simple graph that has no cycles

Answer

A connected, simple graph that has no cycles is called a **tree**. In graph theory, a tree has several important properties:

1. **Acyclic**: It contains no cycles.
2. **Connected**: There is a path between any two vertices.
3. **n-1 Edges**: If the tree has \( n \) vertices, it will have \( n-1 \) edges.
4. **Unique Path**: There is exactly one path between any two vertices.

Would you like more details or have any questions about this concept?

Here are some related questions:

1. What is a spanning tree of a graph?
2. How do you find the minimum spanning tree of a weighted graph?
3. Can a tree have multiple connected components?
4. How does a binary tree differ from a general tree?
5. What is a rooted tree?
6. How can you represent a tree using adjacency lists or matrices?
7. What are some common algorithms for traversing trees?
8. How is the concept of a tree used in computer science?

**Tip:** When dealing with graphs, visualizing them can greatly help in understanding their properties and solving related problems.

Explore the concept of a tree in graph theory, its definition, properties, and applications. A tree is a connected, acyclic graph with unique paths between vertices. Learn more about spanning trees, algorithms for tree traversal, and practical applications in computer science.

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