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Question: Answered & Verified by Expert
A graph $G$ has ' $m$ ' vertices of odd degree and ' $n$ ' vertices of even degree. Then which of the following statements is necessarily true?
MathematicsBasic of MathematicsKCETKCET 2007
Options:
  • A $m+n$ is an odd number
  • B $m+n$ is an even number
  • C $n+1$ is an even number
  • D $m+1$ is an odd number
Solution:
1807 Upvotes Verified Answer
The correct answer is: $m+n$ is an even number
Since, the number of vertices of odd degree is always even and number of even degree is always even. So, $m+n$ is an even number.

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