39.2 |
( a ) |
( i ) |
6 |
( ii ) |
2 |
||
( iii ) |
5 |
||
( b ) |
AE |
||
( c ) |
AE , AF , GF , AC , BC and AD |
||
( d ) |
296 |
||
( e ) |
FG , GA , AB , BC , CD , DA , |
||
AE , EF , FA , AC , CA and AF | |||
( f ) |
638 |
||
39.3 |
( a ) |
( i ) |
3 |
( ii ) |
4 |
||
( iii ) |
3 |
||
( iv ) |
15 minutes |
||
( b ) |
CD , DE , EF , FA , AB , BC , |
||
CA , AG , GD , DE , EG , GB | |||
and BC | |||
( c ) |
183 minutes |
||
( d ) |
( i ) |
B |
|
( ii ) |
CD , DE , EF , FA , AB , BC , CA , AG , GD , DE , EG and GB |
||
( iii ) |
178 minutes |
||
39.4 |
( a ) |
( i ) |
5 |
( ii ) |
2 |
||
( iii ) |
7 |
||
( iv ) |
170 seconds |
||
( b ) |
DE , EF , FG , GH , HA , AB , |
||
BC , CD , DB , BI , ID , DF , FI , | |||
IH and HF | |||
( c ) |
1330 seconds |
||
( d ) |
( i ) |
DE , EF , FG , GH , HA , AB , BC , CD , DB , BI , ID , DF , FI , IH , HF and FD |
|
( ii ) |
1445 seconds |
||
40.1 |
( a ) |
( i ) |
4 |
( ii ) |
A , D |
||
( b ) |
BD |
||
( c ) |
Eulerian trail exists as there |
||
are only two vertices of odd | |||
degrees . | |||
( d ) |
( i ) |
70 |
|
( ii ) |
90 |
||
( e ) |
290 |
||
( f ) |
226 |
||
40.2 |
( a ) |
Eulerian trail does not exist as there are more than two vertices of odd degrees . |
|
( b ) |
�0 1 1 0 1
1�
�
�
� 1 0 1 0 1
0
� �1 1 0 1 1
0� M
� �
� �0 0 1 0 1
1� �1 1 1 1 0
1�
� 1 0 0 1 1
0�
�
�
|
||
( c ) |
12 |
||
( d ) |
CD , AB , AE , AC and EF |
||
( e ) |
205 |
||
( f ) |
290 |
||
( g ) |
255 |
||
40.3 |
( a ) |
( i ) |
4 |
( ii ) |
2 |
||
( b ) |
CD , DE , EF , FA , AF , FA , |
||
AB , BC , CD and DC | |||
( c ) |
159 |
||
( d ) |
78 |
||
( e ) |
78 |
||
40.4 |
( a ) |
Eulerian circuit does not exist as not all vertices are of even degree . |
|
( b ) |
AG |
||
( c ) |
AG , AE , AB , AD , CD and EF |
||
( d ) |
490 |
||
( e ) |
792 |
||
( f ) |
621 |
||