MAD 3305 Midterm: MAD 3305 FIU Exam fk
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Most problems are 10 points each, unless labeled: [5 pts] give an example of g such that k(g) < k1(g), if possible. 2a) state the de nition of the center of a connected graph, z(g). Show that in a tree t , the center z(t ) contains at most 2 vertices. Then, draw its dual, g : state konig"s thm about covers. For max credit, draw an embedding, not necessarily planar. State the revised euler formula for non-planar graphs: true-false. You can assume the graphs below have at least one edge. If g contains no odd cycles, then (g) = 2. The petersen graph is neither planar nor hamiltonian. None of the ve regular polyhedra are bipartite. If g is bipartite, then it is class 1. In any connected graph g, p q 1: choose one proof, state and prove menger"s thm #2 (about edge-disjoint paths).
