A connected graph has nine vertices and twelve edges. Does it have a circuit? Why?

To check:

Whether a connected graph having nine vertices and twelve edges, will have a circuit and give reason also.

Given information:

Connected graph, 9 vertices and 12 edges.

Concept used:

Any tree with n vertices has n−1 edges and total degree is 2(n−1).

Calculation:

Consider a connected graph with nine vertices and twelve edges.

The objective is to find if such a graph has a circuit or not.

For any positive integer n, any tree with n vertices have n−1 edges