What does BFS reveal about the connectivity of a graph?2 pointsThe number of edges between two verticesWhether a graph is Eulerian or notThe existence of a path between two verticesThe number of vertices reachable from a given vertex

Breadth-First Search (BFS) is a graph traversal algorithm that explores all the vertices of a graph in breadth-first order, i.e., it explores all the vertices at the present level before moving on to the vertices at the next level.

1. The number of edges between two vertices: BFS does not directly reveal the number of edges between two vertices. However, it can be used to find the shortest path between two vertices in an unweighted graph, which indirectly gives the minimum number of edges between them.

2. Whether a graph is Eulerian or not: An Eulerian graph is one where you can start at any vertex, traverse every edge once and return to the original vertex. BFS alone cannot determine if a graph is Eulerian or not. This requires checking if all vertices have an even degree, which is not something BFS does.

3. The existence of a path between two vertices: BFS can definitely reveal the existence of a path between two vertices. If a BFS traversal starting from one vertex reaches the other vertex, then a path exists. If the BFS traversal ends without reaching the second vertex, then no path exists.

4. The number of vertices reachable from a given vertex: BFS can also reveal the number of vertices reachable from a given vertex. All the vertices visited during the BFS traversal starting from a given vertex are the vertices reachable from that vertex. The number of vertices visited is the number of vertices reachable.