if g is 2 connected then G\e is connected for every edge

Yes, that’s correct! If a graph \( G \) is **2-connected**, then \( G \setminus e \) (the graph \( G \) with any edge \( e \) removed) is still connected. 

### Explanation:

A graph \( G \) is **2-connected** if:
1. \( G \) is connected, meaning there is a path between any two vertices.
2. \( G \) remains connected even if any one vertex is removed, which implies that \( G \) has no articulation points (a vertex whose removal would disconnect the graph).

Given \( G \) is 2-connected, this means:
- Removing any single edge \( e \) from \( G \) will not disconnect the graph because \( G \) would need to lose a vertex to become disconnected (which it cannot, by definition).
- \( G \) has at least two disjoint paths between any two vertices, so the removal of an edge \( e \) will still leave at least one path between any pair of vertices, thus keeping the graph connected.

Therefore, for a 2-connected graph \( G \), removing any edge \( e \) will leave the graph \( G \setminus e \) connected.

Would you like to explore more about 2-connected graphs or have specific questions about graph connectivity? Here are some related questions you might find interesting:

1. What are the characteristics of a 3-connected graph?
2. How can you prove a graph is 2-connected?
3. Is a complete graph always 2-connected?
4. What is the relationship between 2-connected graphs and cycles?
5. Can a graph be 2-connected if it contains a cut vertex?

**Tip:** Remember, if a graph has a cycle between any two vertices, removing any single edge in that cycle won’t disconnect the graph. This is a handy property to remember when dealing with connectivity.

If G is 2-connected, then G\e is connected for every edge.

Explore the properties of 2-connected graphs in graph theory. Learn why a 2-connected graph remains connected even after the removal of any edge. This concept is vital for understanding connectivity in advanced graph theory. Suitable for Grades 11-12 and college-level students.

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