In an undirected graph, the degree d$($u$)$ of a vertex u is the number of

neighbors u has, or equivalently, the number of edges incident upon it$.$

In a directed graph, we distinguish between the in$-$degree din$($u$),$

which is the number of edges into u$,$ and the out$-$degree dout$($u$),$ the

number of edges leaving u$.$

$($a$)$ Show that in an undirected graph, X

u in V

d$($u$)=2|$E$|.$

$($b$)$ Use part $($a$)$ to show that in an undirected graph, there must be

an even number of vertices whose degree is odd.

$($c$)$ Does a similar statement hold for the number of vertices with

odd in$-$degree in a directed graph?