graph theory

Question

The number of independent sets in a complete graph with n vertices is ____

Comments

minimum vertex cover + independent set=n,.....................(1)

for complete graph MVC= n-1 putting this value in eq(1)

independent set=1.

Answer 1

i think the answer should be n.
Since every vertex is adjacent to every other vertices in a complete graph,the graph is n-colorable.
Now the graph can be partitioned into n sets with each set containing exactly one vertex and holding a color for that vertex.Now each partition with 1 vertex is an independent set ...Hence number of independent sets in a complete graph of n vertices is n

Answer 2

It should be 0 since there won't be any pairwise disjoint vertices in a complete graph.