Skip to content
Related Articles

Related Articles

Improve Article
GATE | GATE-CS-2005 | Question 11
  • Last Updated : 11 Sep, 2014

Let G be a 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 indepenĀ­dent set of G is
(A) 12
(B) 8
(C) Less than 8
(D) More than 12


Answer: (A)

Explanation: Background Explanation:
Vertex cover is a set S of vertices of a graph such that each edge of the graph is incident to at least one vertex of S.
Independent set of a graph is a set of vertices such that none of the vertices in this set have an edge connecting them i.e. no two are adjacent. A single vertex is an independent set, but we are interested in maximum independent set, that is largest set which is independent set.

Relation between Independent Set and Vertex Cover : An interesting fact is, the number of vertices of a graph is equal to its minimum vertex cover number plus the size of a maximum independent set. How? removing all vertices of minimum vertex cover leads to maximum independent set.

So if S is the size of minimum vertex cover of G(V,E) then the size
of maximum independent set of G is |V| – S.

Solution:
size of minimum vertex cover = 8
size of maximum independent set = 20 – 8 =12
Therefore, correct answer is (A).

References :
vertex cover
maximum independent set.

This solution is contributed by Nitika Bansal.

Quiz of this Question

Attention reader! Don’t stop learning now. Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up
Recommended Articles
Page :