Recursive algorithm for planar graph

Question

I have this pseudo-code and I need to understand what it does. It takes some planar graph as input and returns a subset of V (that are the vertexes of the graph). It is clearly recursive, but I don't understand what it does except for the "for" that, I guess, it is a cycle to check the edges starting from 2 vertexes and every time that the condition a=v is satisfied it adds b to a list.

function = function1

input = G(V,E) a planar graph

output = W (a subset of V)

if |V| = 0 then
    retrurn {};
end
else
    v ∈ V ;
    N = {};
    for ((a, b) ∈ E or (b, a) ∈ E) do
        if a = v then
            N = N ∪ {b};
        end
    end
    W1 = {v} ∪ function1(inducedSubgraph(V \ {v}));
    W2 = N ∪ function1(inducedSubgraph(V \ {v} \ N));
    if |W1| < |W2| then
        return W1;
    end
    else
        return W2;
    end
end

I suspect it is something about the vertex cover problem, but I'm not sure