Question

Prove that the sum of the degrees of all vertices in a graph with 10 edges is 20.

Answer 1

for a graph with no parallel edges the sum of the degrees of the vetices is always twice the number of the edges

Answer 2

anyways
let see another way
each edge has must have two vertices as its ends

Answer 3

so each edge contributes 2 to the sum of the degrees of the vertices
hence if the number of edges be e then the sum of the degrees is 2e
hence here for 10 edges its 20

Answer 4

thnks! but could u explain how each edge conytibutes 2 to the sum of the degrees?

Answer 5

@experimentX

Answer 6

http://en.wikipedia.org/wiki/Handshaking_lemma

Answer 7

let \( E(a,b) \) connect \(a\) and \(b\). \( E(a,b) \) adds degree ( 1 \) to both \(a \) and \(b\).
you can show this by induction.

Answer 8

ohhkkki got it thnk u so much!