Question

show that the sum of degree of all the vertices in a graph G,is even.

Answer 1

Answer:

Since each edge is incident on two vertices, it contributes 2to the sum of degree of vertices in graph G. Thus the sum of degrees of all vertices in G is twice the number of edges in G. Hence, n∑i=1degree(vi)=2e.

Step-by-step explanation:

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Answer 2

Answer:

The sum of degree of  all  vertices is even.

Step-by-step explanation:

• The sum of the degrees of all the vertices of a graph is twice the number of edges in the graph.

                         $\sum_{i=1} ^n deg(v_{i} )=2q$

• q represents number of edges in graph G and
• $deg(v_{i} )$ is degree of vertices in graph G

Therefore, any number q which is multiplied by 2 will be always even.

 Sum of degree of  all the vertices in graph G, is always even.