In the beginning, in the family name Graph , there is a point. This point is called a vertex . It is an isolated point of Graph. It feels so lonely.
Then there is another point, which also identifies itself as a vertex. These two points requested to be called vertices.
Now the two vertices are isolated points of a Graph. They are not connected. A graph no needs to be connected.
Teknomo, Kardi (2015) Pictorial Introduction to Graph Theory. http:\\people.revoledu.com\kardi\tutorial\GraphTheory\