| Date | May 2012 | Marks available | 2 | Reference code | 12M.3dm.hl.TZ0.3 |
| Level | HL only | Paper | Paper 3 Discrete mathematics | Time zone | TZ0 |
| Command term | Draw | Question number | 3 | Adapted from | N/A |
Question
The graph G has adjacency matrix M given below.
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.
Markscheme
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]
Examiners report
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.
