Math 3614: Study Guide 3 (9/16-9/25)

Sections 6.6-7.3

Objectives:

1. Learn the following terms: (the starred terms are the most important)
   • partial ordering*
   • poset*
   • total ordering*
   • well-ordered set
   • lexicographic ordering*
   • Hasse diagram*
   • maximal and minimal elements*
   • greatest and least elements*
   • upper and lower bound*
   • greatest lower bound
   • least upper bound
   • lattice
   • topological sort*
   • simple graph
   • multigraph
   • pseudograph
   • directed graph*
   • directed multigraph
   • adjacent vertices
   • incident edge
   • degree of a vertex (be careful how to count loops)*
   • initial vertex
   • terminal vertex
   • in-degree
   • out-degree
   • complete graph
   • cycle*
   • wheels
   • n-cubes*
   • bipartite graphs*
   • subgraph
   • union
2. Become comfortable working the following types of problems:
   1. Given a set and a relation, determine whether they form a poset.
   2. Given a directed graph of a relation, determine whether the relation is a partial ordering. (Hint: look for cycles).
   3. Find the lexicographic ordering of a given set.
   4. Draw the Hasse diagram for a given partial ordering of a set.
   5. Given the Hasse diagram of a poset, find the maximal elements, the minimal elements, the greatest element (if it exists), and the least element (if it exists). Find the least upper bound of a subset of the vertices.
   6. Given an undirected graph, determine the degree of a given vertex.
   7. Given the degrees of all the vertices of an (undirected graph) graph, determine the number of edges of the graph.
   8. Given a simple graph, determine whether it is bipartite.
   9. Represent a multigraph or pseudograph using an incidence matrix.
   10. Given two graphs, determine whether they are isomorphic.
3. Problem List:Learn to work the following problems:
   1. Section 6.6: 6, 15, 20, 31
   2. Section 7.1: 11, 19
   3. Section 7.2: 6, 13-17
   4. Section 7.3: 17, 19, 35, 36

Evaluation:

1. On Monday, September 23, we will have a short competition to reinforce the terminology in these sections. This will not be part of your grade; but will hopefully be fun. The winning group will receive a prize.
2. On Wednesday, September 25, the above objectives will be evaluated with a short quiz. You will take the quiz individually, and your group will be given the average score achieved by the members of your group.