*Know the major algorithms: How to find an Euler path/circuit How to find a minimum spanning tree (Kruskal's algorithm) Greeding Coloring Algorithm *Know major definitions and symbols regarding graphs degree of a vertex minimum and maximum degree of a vertex respectively (lowercase and uppercase greek delta) connected graph planar graph Euler paths and Euler circuits Hamiltonian paths and circuits chromatic number (greek letter "chi") the graphs: P_n, C_n, K_n, K_m,n and how to draw them. gray code of size n = a list of all the sequences of n 0s and 1s so that from one sequence to the next only a single position changes. For example gray code of size 2 might go: 00, 01, 11, 10. Gray code of size 3 might go: 000, 001, 011, 010, 110, 100, 101, 111. *Know the major theorems: +"Euler's Theorem" - all even vertices yields an Euler circuit, two odd yields an Euler path, anything else and there is nothing +"Sum of degrees theorem" - The sum of the degrees of the vertices is twice the number of edges in the graph. +"Friendship Theorem" - Among any 6 people either 3 mutually know each other or there are 3 mutual strangers. +"Planar graph theorem" - a graph is planar iff it contains no copy of K_5 or K_3,3 +"Planar graph invariant" - In a planar graph we have: v - e + f = 2 where v = #vertices, e = #edges, and f = #faces +There is no graph with a single vertex of odd degree. *Know how to work out and solve problems like we did in class *The material from the first website linked this week will be helpful to study, the second is for historical information which will NOT show up on the exam, but MAY be used in the biographical essay for next week. *Keep in mind the applications of these topics that we discussed and any smaller examples I may have worked out to explain something in class. These won't appear as any of the major topics for the exam, but may help you to work through a short answer or true/false question.