MATH 475 Midterm: MATH475 BOYLE-M SPRING2005 0101 MID EXAM
15 Feb 2019
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No books, notes, calculators or electronic devices: (15 pts) a planar graph contains 500 vertices and 8 connected components. The graph divides the plane into 12 regions (including the one unbounded region). How many edges are in the graph: (15 pts) for the n-dimensional hypercube graph gn, the vertex set is the set of all vectors v = (v1, v2, . , vn) such that vi {0, 1} for every i. Gn between vertices v and u if and only if #{i : vi 6= ui} = 1. For which n does gn have an euler trail: (10 points) the game trio is played by three people, with one winner. What is the prufer sequence of g? (b) (15 points) draw the labelled tree on vertices {1, 2, . , 9} whose prufer sequence is (3, 3, 6, 5, 7, 5, 1): (20 points) suppose all labels of a connected labeled graph g are di erent.
