We know that graph is connected when there is a path between every pair of vertices. A graph that is not connected is disconnected. A graph G is said to be disconnected if there exist two nodes in G such that no path in G has those nodes as endpoints.
A cut vertex is a vertex that when removed (with its boundary edges) from a graph creates more components than previously in the graph.
Do we have a graph that each vertex is a cut vertex??
Best Answer
The typical image of the number line, an infinite horizontal line formed from vertices at the integers and edges connecting each integer to its nearest two neighbors, has the property that every vertex is a cut vertex.