UGC NET Dec2020 and June2021 Paper1
October 10, 2023UGC NET Dec2020 and June2021 Paper1
October 10, 2023Nielit ScientistB CS 22072017
Question 2

Which of the following statements is/are TRUE for an undirected graph?
P: Number of odd degree vertices is even
Q: Sum of degrees of all vertices is even
P: Number of odd degree vertices is even
Q: Sum of degrees of all vertices is even
P only


Q only


Both P and Q


Neither P nor Q

Question 2 Explanation:
Euler’s Theorem 3:
The sum of the degrees of all the vertices of a graph is an even number (exactly twice the number of edges).
In every graph, the number of vertices of odd degree must be even.
The sum of the degrees of all the vertices of a graph is an even number (exactly twice the number of edges).
In every graph, the number of vertices of odd degree must be even.
Correct Answer: C
Question 2 Explanation:
Euler’s Theorem 3:
The sum of the degrees of all the vertices of a graph is an even number (exactly twice the number of edges).
In every graph, the number of vertices of odd degree must be even.
The sum of the degrees of all the vertices of a graph is an even number (exactly twice the number of edges).
In every graph, the number of vertices of odd degree must be even.
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