In a finite graph the number of vertices of odd degree is always ______(a) even(b) odd(c) even or odd(d) infiniteThis question was addressed to me during an interview for a job.Origin of the question is Graphs in section Graphs of Discrete Mathematics

In a finite graph the number of vertices of odd degree is always _____

1.	In a finite graph the number of vertices of odd degree is always ______(a) even(b) odd(c) even or odd(d) infiniteThis question was addressed to me during an interview for a job.Origin of the question is Graphs in section Graphs of Discrete Mathematics
Answer» Correct CHOICE is (a) even Easy explanation: In any FINITE graph, sum of degree of all the vertices = 2 * number of edges. Sum of degree of all the vertices with even degree + sum of degree of all the vertices with ODD degree = 2 * number of edges. Now, even number+ sum of degree of all the vertices with odd degree = even number. It is POSSIBLE if and only if number of odd degree vertices are even.

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