Question: Please solve the following using proof of induction and explain each step for my understanding. Thanks! Question 1 (Complete Graphs) Question 2 (Graph Traversal) ---------------------------------------------------------------------------------------------------------------------------------------------

Please solve the following using proof of induction and explain each step for my understanding. Thanks!

Question 1 (Complete Graphs)

Please solve the following using proof of induction and explain each step

Question 2 (Graph Traversal) ---------------------------------------------------------------------------------------------------------------------------------------------

for my understanding. Thanks! Question 1 (Complete Graphs) Question 2 (Graph Traversal)

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) Here is an undirected graph: 2.1 DFS Show the depth-first search tree for this graph if we start the traversal at node \#5. When there is a choice of nodes to explore, explore the one having the smallest node number. (Three points) 2.2 BFS Show the breadth-first search tree for this graph if we start the traversal at node \#5. When there is a choice of nodes to explore, explore the one having the smallest node number. (Three points)

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