You must be able to:
1. state the definitions P(n,r), C(n,r), P(n;r₁,r₂,…,r_m), K_n, K_m,n, graph, connected graph, bipartite graph, directed graph, planar graph, degree of a vertex, two graphs G and G’ are isomorphic, Euler cycle, Hamilton circuit and state Euler’s formula.
2. develop and solve a linear recurrence relation such as 7.1 # 3, 7.3 # 3a.
3. solve basic counting problems such as the more straightforward problems from the homework from chapter 5.
4. use Euler’s formula to determine the number of vertices, edges or regions of a graph.
5. determine if a graph is bipartite or planar (and if not, find a K_3,3 configuration).
6. determine whether two graphs are isomorphic.
7. find the adjacency matrix from a graph or a graph from its adjacency matrix.
8. determine whether a graph has an Euler cycle or path, and a Hamilton circuit.