Homework #7
Due : ********

1. #72 section 6.2 page 284.
   Let G be a connected graph. The distance between vertex v and w in G, dist(v,w),
   is the length of a shortest path from v to w.
   The diameter of G is
   d(G) = max{ dist(v,w) | v and w are vertices on G } .

   Find the diameter of K_n, the complete graph on n vertices.

2. #10 section 6.4 page 291
   Give an example of a graph that has an Euler cycle that is also a Hamiltonian cycle.
3. #36 section 6.4 page 291
   For which n does the complete graph on n vertices have a Hamiltonian path?
4. #5 section 6.4 page 296
5. #17 section 6.5 page 300
   Draw the graph with the given adjacency matrix :
   The 7 X 7 matrix whose i,j th entry is 1 if i+1 divides j+1 or j+1 divides i+1, i ¹ j; where i,i th entry is 2 if i = j and whose i,i th entry is 0 otherwise.
6. #25 section 6.5 page 300