Question

A graph $G$ has ${}^{\prime }{m}^{\prime }$ vertices of odd degree and ${}^{\prime }{n}^{\prime }$ vertices of even degree. Then which of the following statements is necessarily true ?

• 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

Answer 1

Answer: (B)

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.