Draw the graph G .

What information about G is contained in the diagonal elements of M\(^2\) ?

List the trails of length 4 starting at A and ending at C.

     A2

Note: Award A1 if only one error, A0 for two or more.

[2 marks]

the (k, k) element of M\(^2\) is the number of vertices directly connected to vertex k     A1 

Note: Accept comment about the number of walks of length 2, in which the initial and final vertices coincide.

[1 mark]

the trails of length 4 are ABEDC, AFEDC, AFEBC     A1A1A1 

Note: A1A1A1 for three correct with no additions; A1A1A0 for all correct, but with additions; A1A0A0 for two correct with or without additions.

[3 marks]

Parts (a) and (c) were generally correctly answered. In part (b), a minority of candidates failed to mention that the starting and end points had to coincide. A large number of candidates gave all walks (trails were asked for) – an unnecessary loss of marks.

Parts (a) and (c) were generally correctly answered. In part (b), a minority of candidates failed to mention that the starting and end points had to coincide. A large number of candidates gave all walks (trails were asked for) – an unnecessary loss of marks.

Parts (a) and (c) were generally correctly answered. In part (b), a minority of candidates failed to mention that the starting and end points had to coincide. A large number of candidates gave all walks (trails were asked for) – an unnecessary loss of marks.