please help I'm completely lost

Is the following connected graph a tree please explain

There are 4 vertices, two with degree 1,
one with degree 2,
and the degree of the fourth vertex is not known.

To determine if a graph is a tree, we need to first understand the definition of a tree. A tree is an undirected graph with no cycles and is connected. In other words, there is a path between any two vertices in a tree, and there are no loops or repeating edges.

In your case, you have described a graph with 4 vertices, with two vertices having a degree of 1, one vertex with a degree of 2, and the degree of the fourth vertex is not known.

To determine if this graph is a tree, we need to check for the two main conditions: no cycles and connectivity.

1. No cycles: Since the degrees of two vertices are 1, it means these two vertices are leaf nodes, meaning they are endpoints of the graph. This ensures that there are no cycles present within the graph.

2. Connectivity: For a graph to be a tree, it must be connected, meaning there is a path between any two vertices. Since there are only four vertices in the graph, we can consider the possible scenarios:

• If the unknown vertex has a degree of 1, then the graph would have two leaf nodes and a path between all vertices, making it a connected tree.

• If the unknown vertex has a degree of 2, then it would be a center node connecting both leaf nodes. Again, this would result in a connected tree.

• If the unknown vertex has a degree higher than 2, then it would not satisfy the necessary conditions to be a tree because it would create cycles within the graph.

Therefore, based on the given information, if the unknown vertex has a degree of 1 or 2, the graph would be a connected tree. If the unknown vertex has a degree higher than 2, the graph would not be a tree.