Graph-Search: Added initial files

Graph-Search/class-activity.md

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+# 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.
+
+![Graph](./assets/graph.png)
+
+## 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.