Please solve the following using proof of induction. Please also complete the bonus section at the bottom and explain each step for my understanding. Don't copy and paste any previous or similar answer, I want to learn this.Thanks!

A graph G=(V,E) is complete if for all s,tV, there is an edge (s,t)E. Answer these questions: (1) How many edges does a complete graph G having n nodes have? Prove this inductively. State your inductive hypothesis clearly. (Five points) (2) How many iterations of DFS does it take to traverse a complete graph having n nodes? Explain (but don't prove) why this is. (One point) (3) How many iterations of BFS does it take to traverse a complete graph having n nodes? Explain (but don't prove) why this is. (One point) Students taking the course for graduate credit, and undergraduates for a little extra credit, prove the following. Let G be a graph having n nodes, where n is an even number. If every node of G has degree at least n/2, then G is connected