Question

show that the sum of degree of all the vertices in a graph G,is even. please anwer this stepwise​

Answer 1

Answer:

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.

Answer 2

Answer:

Theorem 3.12: In any graph G with e edges, the sum of the degrees of all the vertices = 2e. Theorem 3.13: If T is a tree with more than 1 vertex, there are at least 2 pendant vertices. Pf: Since T is connected, every vertex has degree at least 1.