Draw an example of a graph (with as many vertices, edges as you want) that has at least 3 even vertices and at least 2 odd vertices or state why such a graph is impossible.

Step-by-step explanation:

Consider the provided information.

We need to draw at least 3 even vertices and at least 2 odd vertices.

First understand the even vertices and odd vertices.

Even vertices: If the order of vertices is even then its called even vertices and we can define the order of vertices by counting the number of edges connected to the vertices. Conversely for Odd vertices.

For better understanding refer the figure 1:

Vertices T, R, S and M has odd numbers of edge so they are called odd vertices.

Vertices A has even number of edge so they are called even vertices.

Now we need to draw the the example of a graph that has at least 3 even vertices and at least 2 odd vertices.

Now consider the figure 2:

The figure 2 has 3 even vertices B, C and E. Also the figure 2 has 2 odd vertices A and D.

Hence, the required graph is shown in figure 2.