Draw the graph G whose adjacency matrix is

Does G contain an Eulerian cycle? Does G contain a Hamiltonian cycle? Briefly justify your answers.

The following table gives the distances (in miles) between six towns A, B, C, D, E, and F.

 A B C D E F A — 9 26 25 36 16 B 9 — 22 18 27 20 C 26 22 — 8 30 12 D 25 18 8 — 14 38 E 36 27 30 14 — 28 F 16 20 12 38 28 —

(a) Use the minimal spanning tree algorithm to find a network of minimal total length linking all six towns. What is the total length of the network?

(b) Use the nearest neighbor algorithm (starting at town A) to find a circular route visiting all six towns. What is the total length of the route?

Relations R and S are defined on the set {1, 2, 3, . . . , 12} as follows:

R = {(x, y) : xy = 12} and S = {(x, y) : 2x = 3y}

(a) List the ordered pairs that belong to the composite relation S o R

(b) Determine the logical boolean matrix representing the composite matrix S o R

The knowledge based system TENNIS contains the following list of basic facts:

(a)       ? – am(x) and asks(x, charles)