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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
 musl have. a cash. which
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Wattv once
I a M Musi 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 varHus 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 KuraFowski‘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 varHus ma odd cream, Z 42.300 would [at «to! XGV c. Every trianglefree" graph is bipartite. False k BipovHi'e. Win kas
ho odd Giggles CV "5 M? Bi‘PWh'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. outsML 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 = “huee. is an colaa 2 Gil52.5
if‘ Hang (JVr. hosfile. 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 cosl 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 [Qatar2&5 m‘.C.0I\P\QL;tc__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.
 Spring '09
 COSTELLO
 Math

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