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. ⟹ ∑ni=r+1degree(vi) is even.