What is the definition of a graph? Does every graph have at least one vertex? If so, then how can we create a graph without any vertex or edges using just pencil and paper?

In mathematics, a graph is a collection of vertices or nodes and edges that connect pairs of vertices.

Yes, every graph has at least one vertex, as the vertex is the basic unit of a graph.

However, it is not possible to create a graph without any vertices or edges since a graph is defined as a set of vertices and edges.

If you want to create a graph with no vertices or edges using just a pencil and paper, you could simply draw an empty sheet of paper with no marks on it. While this may not technically be considered a graph, it could be thought of as a "null graph."