WUCT121 Discrete Mathematics Graphs Tutorial Exercises Solutions
WUCT121 Discrete Mathematics Graphs Tutorial Exercises Solutions
WUCT121 Discrete Mathematics Graphs Tutorial Exercises Solutions
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(c) Use Kruskal’s algorithm to find the minimum spanning tree for the following<br />
weighted graph. Write down the number of steps you need to complete the<br />
algorithm<br />
1<br />
v 1<br />
2<br />
v 2<br />
2<br />
1<br />
3<br />
v 3<br />
3<br />
v 4<br />
Edge Weight Will adding<br />
edge make<br />
circuit<br />
1 ( v1,v2<br />
)<br />
2 ( v2,v4<br />
)<br />
3 ( v1,v3<br />
)<br />
4 ( v2,v3)<br />
5 ( v3,v4<br />
)<br />
6 ( v1,v4<br />
)<br />
Action taken<br />
Cumulative<br />
Weight of<br />
Subgraph<br />
e = 1 No Added 1<br />
e = 1 No Added 2<br />
e = 2 No Added 4<br />
e = 2 Yes Not added 4<br />
e = 3 Yes Not added 4<br />
e = 3 Yes Not added 4<br />
Minimum spanning tree is<br />
v 1<br />
v 2<br />
v 3<br />
v 4<br />
The algorithm can be completed in 3 steps.<br />
<strong>WUCT121</strong> <strong>Graphs</strong>: <strong>Tutorial</strong> Exercise <strong>Solutions</strong> 8
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