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IGNOU UNIVERSITY MCA - II (SEM 3) JUN 2009 : Advanced Discrete Mathematics

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I I I I I MCA (Revised) O \O Term-End E xamination june, 2 009 eo O MCS-033: A DVANCED D ISCRETE MATHEMATICS MaxirnumM arks : 5 0 Time : 2 h ours Note : L. Q uestionn o. 1 t s c ompulsory. A ttempt a ny t hree questionsro* the r est. f (a) F ind t he o rder a nd d egree o f t he f ollowing recurrences. A lso, s tate w hether t hey a re homogeneous o r n on h omogeneous (t) a a r.,:ar., o*a.-l (ii) ar:sin f l1 e ....* d o % ( n> 2 ) or-1*cos dr-2*sin ?r*3 * . . . .* e r (b) MCS-033 S how t hat t he s um o f t he d egrees o f a ll vertices of a graph is twice the number of edges in the graph. P.T.O. (c) (d) S olve (u) F ind a g enerating f unction t o c ount t he number o f i nteger s olutions t o er* e 2* e z:10 i f f or e achi , o sei (f) What is the complement of the given graph ( u) I n a c omplete g raph w ith n v ertices t here are ( n - 1)/2 e dge d isjoint H amiltonian circuits, i f n i s a n o dd n umber ) 3 . (b) 2. Define isomorphism of graphs. Determine whether the graphs are isomoryhic. S olve a n - 6 un_, + 8 ar., z:3n _ t he r ecurrence uzn-2u'n-1:L f or n 21, d o:2 and ar-/ MCS-033 r elation w here a o:3 3. ( u) Which c onnected g raphs c an b e b oth regular a nd b ipartite a nd w hy ? (b) How m any v ertices w ill t he f ollowing graphs have if they contain : (i) (ii) (c) 1 6 e dgesa nd a ll v erticeso f d egree2 . 2 1 e dges,3 v ertices o f d egree 4 a nd the other vertices of degree 3 Find the chromatic number of the following graph 4. (u) S olve t he f ollowing r ecurrence r elation b y substitution m ethod d n : d n _ + n 2 w here t do= 7 (b) Define s panning f ree w ith a n e xample. (c) Solve : a ,., 6an_1 * 1 .2an_2+8ar.,_30 : * MCS-033 3 P.T.O.

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Additional Info : Mca - II (sem 3) June 2009 Question Paper - Advanced Discrete Mathematics (Revised Course)
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