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

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I MCS-033 I MCA (Revised) Term-End Examination December, 2009 MCS-033 : ADVANCED DISCRETE MATHEMATICS Maximum Marks : 50 Time : 2 hours Note : 1. Question no. 1 is compulsory. Attempt any three questions from the rest. (a) Determine the number of subsets of a set of n elements, n 3 O. The number of vertices of odd degree in a graph is always even. What is the complement of the given graph e b (d) Solve the recurrence relation a n 2a n _ 1 3a n _ 2 = 0, n 2 with ao = 3 and a l = 1 MCS-033 1 4 3 4 P.T.O. Show that a complete graph kn is planar if 4 n5.4. Let f(n)= 5 f(n/ 2) + 3 and f(1) = 7. Find f(2k) where k is a positive integer. Also estimate f(n) if f is an increasing function. 2. Determine whether the graphs are isomorphic. (a) 3 4 b z Zh V H Solve the recurrence relation 4 S r 4Sr r _ 1 + 4S r = (1 + r)2r What is the chromatic number of the following graph. MCS-033 2 2 3. (a) Find the order and degree of the following recurrence relations. Also find whether they are homogeneous or non homogeneous ? ( i ) ll 4 a n 3a n-i + n2 Sn =S2n_i Sn-2 Sn-3 Sn -4 Show that the graph given below does not contain a Himiltonian cycle. a 3 (c) Whether the following graph contains Euler circuit a : a 3 (b) h 4. (a) Solve the following recurrence relation using generating function. 5 a n - 9a n + 20a n _ 2 = 0 for n 2, a t) = - 3 and a 1 = -10 (b) What is the largest number of vertices in a graph with 35 edges if all vertices are of degree at least 3 ? MCS - 033 3 5 P.T.O. 5. (a) Suppose a tree has n 1 vertices of degree 1, 2 vertices of degree, 2, 4 vertices of degree 3 and 3 vertices of degree 4, find n1. Find the solution of a, ra,, 5 a n _T + 6\17 = 0, n 2 where ao = 4 and a 1 = 25 Find the generating function of the following function. a = 2r + 3, r = -o0o- MCS-033 4 3 5

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