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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
  • a)
    k and n
  • b)
    k - 1 and k + 1
  • c)
    k - 1 and n - 1
  • d)
    k + 1 and n - k
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let G be an arbitrary graph with n nodes and k components. If a vertex...
Minimum: The removed vertex itself is a separate connected component. So removal of a vertex creates k-1 components. Maximum: It may be possible that the removed vertex disconnects all components. For example the removed vertex is center of a star. So removal creates n-1 components.
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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 betweena)k and nb)k - 1 and k + 1c)k - 1 and n - 1d)k + 1 and n - kCorrect answer is option 'C'. Can you explain this answer?
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