In each of 8—21, either draw a graph with the given specifications or explain why no such graph exists.

15. Graph, circuit-free, seven vertices, four edges

To draw:

A graph with the given specifications and also explain if no such type of graph exists.

Given information:

Graph, circuit-free, seven vertices, four edges.

Concept used:

For any positive integer n, if G is a connected graph with n vertices and n−1 edges, then G is a tree.

Calculation:

The objective is to draw a graph with seven vertices, four edges and circuit-free if possible else explain the reason why such graph does not exist.

The following graph satisfies all the features mentioned above.

That is, the graph has seven vertices namely, a,b,c,d,e,f and g