test3_solutions

# test3_solutions - Test 3 ' Name: Keﬁ Math 2602 arch 30,...

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Unformatted text preview: Test 3 ' Name: Keﬁ Math 2602 arch 30, 2006 There are no calculators allowed during the test. This test is closed notes and ciosed book. Explain all your work.- (Use actual words.) f: be‘bw 1. (12 points) Please give an example of the following simple graphs: and“ af- M has mug Fossil)“, Carder? QHSWS_ a. A Hamiltonian graph which is not Eulerian - mus-l- have. a cash. which E Pnsus {‘kvauah and» waft“ Watt-v once I a M Mus-i- bevcr‘l'ices w‘ﬁk Odd degree ' I b. An Eulerian graph which is not Hamiltonian ' "95+ lam W m. o a. (33:19 05%.? all W+§m§ Duct. and OnLD ant-.9, can't- axis} 0. A planar drawing of a graph G with MG) : 4 and n =' 8' 5“de means M is o.» G [<1] SOEJY'ufla' h“? 3 var-Hus UIO 60192.5 My cra\$s f... boob df'GWl'ﬂj 2. (10 points) Below is a weighted graph G and the first rows in an instance of Dijkstra’s algorithm to calculate distances from the vertex A. a. Fill in the next two rows in this chart. 3 . b. Whatiis the shortest path between vertices A and F? ( _A—c—E~F 3. (9 points) ‘ Each of the following statements is either true or false. if true, state a theorem to justify, if false give a counter example. a. A graph G with MG) 2 5 cannot be planar. 'True. by Kura-Fowski‘s Tkm 0“ by L'E‘COlor‘ b. A simple graph cannot have exactly 3 vertices of odd degree. True Since. Zdestx) =‘- 2. [El . Kev H” 3 var-Hus ma odd cream, Z 42.300 would [at «to! XGV c. Every triangle-free" graph is bipartite. False- k Bipov-Hi'e. Win kas ho odd Giggles CV "5 M? Bi‘PW-h'tc, but is +ri~jhf¥fte 4. (8 points) a. Give the coloring number for this graph and justify yeur answer! %= «0(6) 5—.ch 5mm hm. outs-ML is an odd Cng U36 W0“) 'w sang, ’33 colors ‘t’b color“ , GM Shaw whiz is (1&3qu h b. Show a minimum spanning tree in this graph and give its total weight: (“ML 6“ 5. (16 points) For each question, ﬁll in the blank and also list what the vertices and edges repre- sent in the appropriate gra hs. ‘ “Those \$U€S+ions Owe Mu Hi pie. eolu+ions in some, Cases. : a. Two cities are called “hostile” if there is a sports team rivalry between them. You have a group of sports fans, and want to find out how many tour groups I need to form so there are no two people from hostile cities in a tour group to- gether. I want to design the appropriate graph and find Wer- - V== cities E = “hue-e. is an colaa 2 Gil-52.5 if‘ Hang (JV-r. hos-file. b. l have a list of cities and the cost to travel between each pair of cities. If I want to attend a ball game in each city i want to design the appropriate graph and find TS [ ( Irgglfwb SqLLs ma.» +oor‘) V: Cif'u. S . ‘ Ea Coan/h'cns balm cities whim weights for cos-l c. I am in a zoo. Each animal exhibit has a train line that goes by it. I want to make sure I see all the animals! Each train station has 4 routes (you can travel a route in either direction). I want to design the appropriate graph and find Eu +€ain Sﬁa‘l'r‘ons d. In a group of multilingual studentsf two languages are "connected" if there is at least one person who can speak both languages. I want to make sure that if I give an announcement in one language everyone has it translated to them using the smallest number of translations. 3| want to design the appropriate graph and find ﬁpagniﬂa ta Q, V : lanjuagas E: We [Qatar-2&5 m‘.-C.0I\P\QL;t-c__cq H: MAL-{S Sombm NM: SPeQLS laU'HW '1' ...
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## This note was uploaded on 11/08/2009 for the course MATH 2602 taught by Professor Costello during the Spring '09 term at Georgia Tech.

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test3_solutions - Test 3 ' Name: Keﬁ Math 2602 arch 30,...

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