2.1 KiB
Class Activity: Exploring MST Characteristics
We will be exploring creating graphs that showcase different aspects of MST algorithms.
Task 1:
True/False. A MST can sometimes contain a cycle. Justify your answer with one or two sentences.
Answer: False. By definition you can remove an edge from cycle and all vertices will still be connected. Therefor if the MST has a cycle in it then that would mean it has a redundant edge and is therefore not minimal.
Task 2:
For the following graph, show the safe data structure after one call to
Borůvka's AddAllSafeEdges method. Draw the spanning tree F showing all of the
safe edges that were added to it after this first pass.
Task 3:
Create a graph with at least 6 nodes that is fully connected (a complete graph)
and has distinct edge weights that Boruvka's algorithm can solve in a single
call to AddAllSafeEdges. Submit a picture of the graph and the safe array/list
that is created by the call to AddAllSafeEdges.
Task 4:
Create a graph with at least 6 vertices with distinct edge weights such that the MST contains the edge with the largest weight. Submit a picture of this graph.
Task 5:
Create a graph with at least 4 nodes that is fully connected (a complete graph)
and has distinct edge weights that Boruvka's algorithm exhibits its worst case
performance. First, define what the worst case perform is for a single call to
AddAllSafeEdges. Next, showcase this performance on your graph clearly showing
how the MST (F) looks after a single call to AddAllSafeEdges and showing the
contents of the array/list safe.
Task 6:
Can you create a graph with at least 4 vertices with distinct edge weights such
that the MST does not contain the lightest edge? Explain your answer both
logically (1 to 2 sentences) and using the logic within Boruvka's
AddAllSafeEdges.
Submission
Submit a picture of your answers to this canvas assignment. If you worked with another person, acknowledge that by placing the names of all people you worked with at the top of the first page of your submission.