Suppose we have a graph $G(V,E)$ 

[![enter image description here][1]][1]

What is the number of independent sets in graph of this type?

I have an idea to use reccurence
$$|G|=|G\backslash \{v\}|+|G\backslash n(v)|$$
where $|G|$ is the number all possible independent sets of graph G,
$v$ is an arbitrary vertex, and $n(v)$ is a set of all vertex's joined to $v$ and $v$ itself.

But may be there some better ideas or results?


  [1]: https://i.sstatic.net/K7gI2.png