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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 indepen­dent set of G is
  • a)
    12
  • b)
    8
  • c)
    Less than 8
  • d)
    More than 12
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let G be a simple graph with 20 vertices and 100 edges. The size of th...
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.
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Most Upvoted Answer
Let G be a simple graph with 20 vertices and 100 edges. The size of th...
Explanation:

  • A vertex cover is a set of vertices that includes at least one endpoint of every edge in the graph.

  • In a simple graph, the size of the minimum vertex cover is equal to the size of the maximum matching.

  • Therefore, in this case, the size of the maximum matching is 8.

  • An independent set is a set of vertices in which no two vertices are adjacent.

  • The complement of an independent set is a vertex cover.

  • Therefore, the size of the minimum vertex cover plus the size of the maximum independent set is equal to the number of vertices in the graph.

  • Hence, the size of the maximum independent set is 20 - 8 = 12.

  • Therefore, the correct option is (a) 12.

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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 indepen­dent set of G isa)12b)8c)Less than 8d)More than 12Correct answer is option 'A'. Can you explain this answer?
Question Description
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 indepen­dent set of G isa)12b)8c)Less than 8d)More than 12Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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 indepen­dent set of G isa)12b)8c)Less than 8d)More than 12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 indepen­dent set of G isa)12b)8c)Less than 8d)More than 12Correct answer is option 'A'. Can you explain this answer?.
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