I have found the proof that if G is a simple graph with order $n\geq 2$ then there are at least two vertices in $V(G)$ that have equal degree. Does this statement extend to non-simple graphs? If so, how do I go about proving it? Thank you
Suppose you construct a graph with three vertices $a,b,c$.
$a$ is having a self loop and is connected to $b$, $b$ is having a self loop and connected to $c$.
Degree($a$) =$ 3$, Degree($b$) =$ 4$, Degree($c$) =$1$