A graph G has 21 edges, 3 vertices of degree 4 and other vertices are of degree 3. Findthe number of vertices in G.

To find the number of vertices in graph G, we need to use the Handshaking Theorem. The Handshaking Theorem states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

In this case, we know that the graph has 21 edges and that 3 vertices have a degree of 4. So, the sum of the degrees of these 3 vertices is 3*4 = 12.

Let's denote the remaining vertices as x. These vertices have a degree of 3. So, the sum of the degrees of these vertices is 3x.

According to the Handshaking Theorem, the sum of the degrees of all vertices is equal to twice the number of edges. So, we have:

12 + 3x = 2*21 12 + 3x = 42 3x = 42 - 12 3x = 30 x = 30 / 3 x = 10

So, there are 10 vertices of degree 3.

In total, the graph has 3 + 10 = 13 vertices.