### coefficient of smallest power of $x$ in the adjacency characteristic polynomial of $g$ is $1$

This shows connected graphs on 7 vertices
with nonsingular adjacency matrix.

```
for g in graphs.nauty_geng('7 -c'):
if
```~~g.adjacency_matrix().determinant()==0:
~~g.adjacency_matrix().determinant() == 0:
~~t=g.adjacency_matrix().charpoly()
~~t = g.adjacency_matrix().charpoly()
g.show()
~~print(t)~~print(t)

Using the above code, how we can obtain only those ~~graphs ~~graphs
(if any) satisfying the following property: coefficient ~~of ~~of
smallest power of $x$ in the adjacency ~~characteristic ~~characteristic
polynomial of $g$ is ~~$1$~~$1$.