Let $$G$$ be the simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of $$G$$ is 8. Then, the size of the maximum independent set of $$G$$ is:

Let $$G$$ be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is:

What is the maximum number of edges in an acyclic undirected graph with $$n$$ vertices?

Let $$G$$ be an arbitrary graph with $$n$$ nodes and $$k$$ components. If a vertex is removed from $$G$$, the number of components in the resultant graph must necessarily lie between