In an undirected graph, if we add the degrees of all vertices, it is:

Question

Question

This question was previously asked in

NIELIT Scientific Assistant A Official Paper 2020

Answer 1

Data:

For an undirected graph

sum of degree in a graph = dsum

number of edges in a graph = e

Formula:

By handshaking lemma:

dsum = 2 × e

Conclustion:

if e is even

dsum = 2 × even = even

if e is odd

dsum = 2 × odd = even

In an undirected graph, if we add the degrees of all vertices, it is even