{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Quiz6_Solution

# Quiz6_Solution - 50 differ MATH2602 — Quiz#6 June 24 2009...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 50 differ) MATH2602 — Quiz #6 _ June 24; 2009 Name: GTID: Each problem is worth 10 points. Show all of your work, and try to be as neat as possible. Points may be deducted if solutions are unclean Use the back of the paper if you need more Space. Problem 1 Determine whether the following graph is Hamiltonian. Either number the vertices so as to indicate a Hamiltonian cycle or explain why no each cycle emists. TEF- 1’ ' "at H ‘ 'n. 5 ' - 75¢ - ”fl" is —- WM W C— ., mm v3 pémh a cyan. m G - _ ‘ dgtvlj=dv(vl)=2, @“Vﬂq ’VIVQ’Vz’Vz’Wquc I. Sine. 42., (3 alga/J aﬂwl' (Vi/'5 ("VJ 4‘17.“ , 1"!”3: qu;_; 121,116 ’56 . wO’LA’" 4/31): ,1/3 "V1 6' C" 50 11'qu3 “Vs a); 1/415 :5 aqua. in C and! ﬁﬁ) a mf/ACL'CIIW? .- ‘ Problem 2 Suppose G is a graph with n certices, and A is its adjacency matrix. Show 'that . Til. T1. 8 X # four cycles in the graph G : (2(A4)i,i — 2(A2)ii m 2 i (A2)i',j) . i=1 i=1 i,j=1,i#j (for example, # four cycles in C4 :1, 0r # four cycles in K4 =3.) (Hint: Exclude all of the walks of length four which are not a cycle in G.) n. [aha Is we «w #4 we: oft-gm,» a. m. .0 id ' bkuk’ Wad-ex "if : We have {our #511“! («S-c5 Mh'c/J M. to a Walk 0: (“337 ‘i‘ é’ ﬂaky af M @ o--- : Inwwr #of ﬁt? I“)!!! of W14- ;(ﬂ )‘lt. V. II. ‘ n luff z I; II ’I Z (A )t. ‘ (9 _- Vuaalf ‘3‘” if). U . V a t ’7 I; n 2 H——a (“73" a I] I n n 7' .- 7, (14%;) :C) V czmq)_'_(z‘cn)m+£Z-; i} a V a 1' 0 ‘1‘ ‘5' {If}. 3 17' ll : 571113 I, is] a CL _ % ch 4—6 dz 8 ﬁms " _ Bui' M Cum-mt 4“ Y ’ , 1H" 3 m. (emf 75m doth/tie é Weft/admic . . W f” W‘ W ”5"” 74"” l'd‘ﬁmi 5 ’3 75:3 Cam/aide: at mf- ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern