MCS033- SOLVED ASSIGNMENT 2016-17 IGNOU MCA3rd SEM

1.

Solve the following recurrence relation through substitution.

(i) an = an-1 + 5, subject to initial condition a1 = 2

(ii) Sn = 5 Sn-1, subject to initial condition S0 = 1

2.

Draw these graphs

(i) C6, (ii) W6 (iii) Q3 (iv) K4,4 (v) K6

3.

For which value of n are these graph regular ? (a) Kn (b) Cn (c) Wn (d) Qn

4.

Draw five subgraphs of the following graph

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6.

Find the order and degree of the following recurrence relation. Also, determine whether they are homogeneous or non-homogeneous. Constant coefficient and non constant coefficient. (i) an = nan-1 + n2an-2 + an-1 an-2 (ii) an = 5 an-1 + n3 (iii) an = C an/m + b (iv) an = nan-1 + n2an-2 + an-1 an-2 (v) an = C1 an-1 + C2 an-2+ ….. Cn-k an-k

7.

A person invests Rs. 10,000 at 10 percent interest compounded annually. If An represents the amount at the end of n years, find a recurrence relation and initial condition that define the sequence {An}. Using the recurrence relation find amount payable after five years.

8.

State Dirac's and Ore's Theorem.

9.

Determine whether the directed graph shown below has an Euler circuit. Construct an Euler circuit if one exists, if no Euler circuit exists, determine when the directed graph has Euler path. If yes, construct an Euler path if one exists.

10.

What is the solution of the recurrence relation An = an-1 + 2 an-2 With a0 = 2 and a1 = 7

11.

Define bipartite graph. Also given an example of it, where do you use this type of graph.

12.

What is the chromatic number of the following graph ?

13.

Solve the following recurrence relation by substitution tn = tn-1 + n for n > 1 t1 = 1

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