so I've come across a weird problem. I've learned about induction before, and when it's an equation I can generally do them. However, this problem I'm having trouble with:
"A k-regular graph is an undirected graph where every vertex has degree k. For example, a graph with 3 vertices connected in a triangle is a 2-regular graph, since each vertex has degree 2. Use induction to show that for every k ≥ 1, there exists a k-regular graph."
I figured I'd give the base step by showing a graph with two points and a single line connecting them to show k = 1. Not really sure where to go from there though or if that's even the case. I'm having a hard time just coming up with a hypothesis for it really. Any direction at all on this will be greatly appreciated it!