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IGNOU UNIVERSITY MCA - II (SEM 3) DEC 2008 : Advanced Discrete Mathematics

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MCA ( Revised) (o (o Term-EndExamination December,2008 @ =f O MCS - 0 33:A DVANCED D ISCRETE MATHEMATICS Time : 2 hours Note : 1. MaximumM arks : 50 Q uestionn o.7 i s c ompulsory. A ttempt a ny t hree questionsorm the rest. f ( u) S how t hat t he g raphs G a nd G 1 a re isomorphic 61 c1 o) Draw three spanningtree of the graph. oV' B )s6 ( c) Solve the recurrence relation tn=4(tn-1- tn-z) subject to initial condition tn:L fOtn=0 and n=L (d) Find t he c hromatic n umber o f f ollowing graph. (e) Find the general solution of ar- 7a ,- , + 1 ,0a, 2 : 7 .3r,r > 2 - (f) Which o f t he f ollowing r epresent t he s e q u e n cL , 2 , 5 , 1 1 , 2 6 , e (0 tn: tn-t* tn-z (ii) t n: t n-7+3tn-z (n0 tn:Ztn_r+L (iv) tn:2tr-L+2 to=7, t r:2 tg :L , t 1:2 to=L, t r:2 tg=L, t 1:2 (u) Show that for a subgraph H of a graph G, ^ ( H)< ^ ( G). (b) Show that K5 is nonplanar. (") Show that the following graph is Euler. Also find Euler Path. "N, 3 3 ( a) d Solvet he r ecurrences n:an-7*5n, a o:1. (b) 3. Find the order, degreehomogeneousor not for following recurence. an-3 an-4 (1) (ii) 4. (a) ar:an--o2n-1.*ar-2 I an: arag* an 1+ ....... aoar(n>2) A c onnected p lane g raph h as 1 0 v ertices each of degtee 3. Into how many regions, does a representation of this planar graph split the plane ? (b) Find an Eular path in the graph : t\ (.) Solve the recurrence a n - 6 a ,- r * 1 2 a n 2 - 8 a n 3 : 0 . - J. (a) S uppose a c oin i s f lipped u ntil 2 h eads appear a nd t hen t he e xperiment s tops. Find a recurrence relation for the number of experiment that end on the ntr flip or sooner ? J 5 (b) Find the solution of following recurrence relation by substitution method. tr:1 and (c) for n:0 tn: t n-1,+n Define K- critical graph. -oOo- f or n >'L. 2

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Additional Info : Mca - II (sem 3) December 2008 Question Paper - Advanced Discrete Mathematics (Revised Course)
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