What is the relationship between vertex connectivity and independent set of a connected graph?

Suppose we have a graph on $20$ vertices which is connected.

If the independent set has cardinality $3$ what can we conclude about the vertex connectivity of the graph?

Another question :

Is there any algorithm to find the separating set of a graph?

Given a graph $G$ does there exist any command in SageMath or in any other software which can say the minimum separating set of a graph?