###### UGC NET Dec-2020 and June-2021 Paper-1

October 10, 2023###### UGC NET Dec-2020 and June-2021 Paper-1

October 10, 2023# Nielit Scientist-B CS 22-07-2017

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 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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