Does there exist a connected graph G such that G has an isol

Does there exist a connected graph G such that G has an isolated vertex? If so, draw a G. If not, state your reasoning as to why no such G exists.

Solution

An isolated vertex which is not connected to any vertex in the graph.

Since in a connected graph there is a path between any two vertices in the graph, it is not possible to have an isolated vertex in a connected graph.

So, sonuch graph G exists which is connected and has an isolated vertex.