soluq3 - Student ID: MA238 Winter 2009 —— Quiz 3 Total...

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Unformatted text preview: Student ID: MA238 Winter 2009 —— Quiz 3 Total marks is . Answer all questions in the spaces provided. Calculators are not permitted. CD [ marks] 1. (a) What is the definition of an Euler path? A A IEU-lc,’ [pa-H“ it a path #4410 3'19 l «my a4" 6‘ Mac-flu], an“, 69 [ marks] (b) Do the following graphs have an Euler circuit? If so, find such a circuit. If it does not, give an argument to show why no such circuit exists. D‘l’er circuit: an: Vorsfbu @ [ marks] 2. List all the different 2-bit Gray codes which begin with the bit string 00. l’hit Gm? adu- cz-rrlepn.) -+5 chl'l‘l‘u/x Cfrgygl'qtd‘ 1k Q1— 60 u! Qi— — 4w Hamlith Llrcmfi'll: :g @L i/ | a “'00 °-o DO lo ll 01 @ [ marks] 3. For which values of m and n does the complete bipartite graph Km,” have a Hamilton circuit? _ 794"“ ‘3 g: m an: «42,-, A Ham IH‘vr alrouq'vf’ “‘1 4— A' ardpA Ila-H?" Ir 4'6/'* 76». V-U 'L'La; {A m P M+5 «avnmaji’mf “ l . Lil'barf -’. M,” 7/ 2‘ V Qua rm "Mt-‘6' “IV/y (Land/fun, mm '5 Alta/y; M y‘ak' W 6”“wa [1 Ht muffin-.1; owe a.) 41 .. at f o ‘ ands LlJ£3/";JAh L.'h< aflb, 4Law ) )0“ A I“ raPL See Reverse '/ an» Zmaw C9 [ marks] 4‘ (a) Does the following graph have a Hamilton circuit? If so, find such a circuit. If it does not, give an argument to show why no such circuit exists. a c a thlll‘h- (affect-{4’ V 1144 AN? l‘lkmil’lbw Ciao—Ii Mir-5" fis‘l’ h K in 4;... 33:590. “H‘s: Va;- “(.25 4-4". a.” a; mm“.._--.... M. e 3 i? cigar“; 3- 0-“ édgflfi‘ (hafJ-cml {g V “Huang MMM l‘rvtlus’fiba 7r» (iii—cum“. (“Wren-“m aM ‘HM a» V firluwd 'H-e which sic-«.132 2:?” "\(Jud-‘d 7 TL“: ‘ ‘L Giraud/l bu'l’ H’ Joe: M 1L; Vavrl'x’ms in» he r 2+ @ falls [ marks] (b) Does the graph have a Hamilton If so, find such a chant. If it does not, give an argument to show why no such eineuit exists. (jg: abcvtapothl/jklomfl‘c / VV Q) [ marks] 5. (a) What is thc definition of a tournament? A low-«VAQWVIJ a 56%ng JI/t EMLM M I( u I, i r” t . x _ e . l N V M \Mr‘lxu'. M +14. Graph} «trad-H3 a M o Q'MA M5} (S M 0C “1 Z [gigs] (b) What is the sum of the in—degree and the Out—degree of a vertex in a tournament? n Vtr'h’LQS . UV‘SK‘J ‘93 M1 arming”. Cor-sfobr a,- arloi’l‘ran? var ink v . Er a—(( 0H.” “q.g\.c_¢ u L affiP‘y‘ Ll‘l’k4r {V203 av (HI v it an», in. 414 a!“ mum £71m fifl’rgv) 4» A”, “WE = .h_ l V ...
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soluq3 - Student ID: MA238 Winter 2009 —— Quiz 3 Total...

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