184a_01f_fe

184a_01f_fe - Math 184A Final Exam 5 December 2001 • Please put your name and ID number on your blue book • The exam is CLOSED BOOK but you may

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Unformatted text preview: Math 184A Final Exam 5 December 2001 • Please put your name and ID number on your blue book. • The exam is CLOSED BOOK, but you may have two pages of notes. • Calculators are NOT allowed. • You must show your work to receive credit. 1. In each case, give an example or explain why none exists . (a) A permutation f of { 1 , 2 , 3 , 4 , 5 } such that f 20 has no fixed points. (b) A simple graph with 8 vertices, 2 connected components and 12 edges. (c) A connected simple graph with 8 vertices, 8 edges and no cycles. 2. Let V = { 1 , 2 , . . . , n } . An oriented simple graph with vertex set V is a simple graph with vertex set V where each edge is given a direction. In other words, given two vertices v and w in V , there are three choices: (a) no edge between them, (b) an edge ( v, w ) or (c) an edge ( w, v ). (Unlike a directed graph, you cannot have both ( v, w ) and ( w, v ) as edges and you cannot have loops.) Let N = ( n 2 ) . We showed that there are 2 N simple graphs with vertex set...
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This note was uploaded on 06/18/2009 for the course MATH 184a taught by Professor Staff during the Fall '08 term at UCSD.

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184a_01f_fe - Math 184A Final Exam 5 December 2001 • Please put your name and ID number on your blue book • The exam is CLOSED BOOK but you may

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