An independent set of a graph G is a subset I of the vertex set V such that no two vertices in I are adjacent. Let i(G) be the size of a maximal independent set of G. (a) Show that I is an independent set of G if and only if V – I is a vertex cover of G. (b) Conclude from part (a) that i(G) + vc(G) = |V|.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
3. An independent set of a graph G is a subset I of the vertex set V such that no two
vertices in I are adjacent. Let i(G) be the size of a maximal independent set of G.
(a) Show that I is an independent set of G if and only if V – I is a vertex cover
of G.
(b) Conclude from part (a) that i(G) + vc(G) = |V|.
Transcribed Image Text:3. An independent set of a graph G is a subset I of the vertex set V such that no two vertices in I are adjacent. Let i(G) be the size of a maximal independent set of G. (a) Show that I is an independent set of G if and only if V – I is a vertex cover of G. (b) Conclude from part (a) that i(G) + vc(G) = |V|.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,