Please give me your own writting solutions for problem 3, not other's, thank you!

3. Let n 2 3. Prove that a graph with n vertices is Hamiltonian if it has at least (", ) + 2 edges. Give an example of a non-hamiltonian graph with n vertices and (", ) + 1 edges (The example must be given for the general case, not only for a specific value of n). 4. Let two graphs G = (V, E) and H = (W, F) be drawn on a paper. Define a new graph KG,# by joining every vertex