1. Chapter 4 sections 1 and 2

4.  Fig. 1  Not connected  All vertices are even.  Fig. 2  Connected  All vertices are even.

6.  1. A graph with four even vertices.  2. A graph with four odd vertices.  3. A graph with three odd vertices.  4. A graph with four vertices of degree two and two vertices of degree three.

7.  1. Four vertices without any edges.  2.  3. Impossible  4.

9. AB  Duplicate edges: BD, ED  FABCD BDAED EF

10.  How many hamilton circuits are there in K 7 ?  Draw a K 6.

11.  1. 6! = 720  2.

12.  Using the 3 methods to find the Hamiltonian circuit.  List the circuit and the total weight.  Start at vertex A.

13. AB =13; AF = 2; AD = 9; AE = 15; AC = 12 BF = 10; BE = 14; BD = 7; BC = 4 CD = 16; CE = 6; CF = 3 DE = 8; DF = 11 EF = 5