MATH203-1402B-04 : Applications of Discrete Mathematics - PHASE 3 IP - Speech or Presentation Example

Based on this, we are thus only able to obtain the following sequences of vertices; We now find the number of simple paths that are associated with the sequence (i) of the vertices as . In a similar way we obtain the number of simple paths that are associated to (ii) is, . The number of simple paths of the sequences associated to (iii) are given is,. Lastly the number of simple paths associated to (iv) is . Based on all these, we can thus obtain the number of simple path sequences that are connected to 1 and 5 to be given as; .

The graph above presents the tree diagram. Being a tree diagram each vertex given corresponds to a mentioned person (for instance, P stands for president, VP stands for vice-president, and so on). It is therefore clear that the many vertices represent the many persons mentioned. We see that for any two given vertices to be connected there must be a direct working relationship/association between the persons who corresponds to the given vertices. For instance if by any chance the direct relationship/association between say the college president and the head of alumni relations is added, then we expect to obtain a graph which is not a tree, this is because, according to the definition, an undirected graph is called a tree if any of the two vertices are connected exactly by one simple path.

In the obtained new graph however, the vertices AR and P are connected by two simple paths