IGNOU MCA -mcs-033 solved assignments 2012 -2013

Course Code : MCS-033

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Course Code   : MCS-033
Course Title :  Advanced Discrete Mathematics
Assignment Number  :  MCA(3)/033/Assign/2012
Maximum Marks :  100
Weightage  :  25%
Last Dates for Submission : 15
th
October, 2012 (For July 2012 Session)
15
th
April, 2013 (For January 2013 Session)
There are FIVE questions of total 80 marks in this assignment. Answer all
questions. 20 Marks are for viva-voce. You may use illustrations and diagrams to
enhance explanations. Please go through the guidelines regarding assignments given
in the Programme Guide for the format of presentation.
Question 1: (a) Using Karnaugh map, simplify
X': A'BC'D'+ ABCD+ ABCD'+ ABCD'  (5 Marks)
(b) Describe Konigsberg’s 7 bridges problem  and Euler's
solution  to  it. B                  (5 Marks)
(c) Show  that  the sum of  the degrees  of all vertices of a
graph  is twice the number of edges  in  the graph.  (5 Marks)
Question 2: (a) Let G be a non directed graph with 12 edges. If G has 5
vertices each of degree 3 and the rest   have degree less
than 3, what is the minimum number of vertices G
can have?          (5 Marks)
(b) What is Graph Cloning? Explain K-edge cloning with
an example.                                   (5 Marks)
(c) 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.        (5 Marks)
Question 3: (a) Define r-regular graph. Give an example of 3-regular
graph.                                            (5 Marks)
(b)                  
f is bijective function with Range of f as the
(5 Marks)6
(c) What are isomorphic graphs? Are the graphs given below isomorphic?
Explain why?      (7 Marks)
(i)                                                                 (ii)
(d) What is connected Graph? Construct a graph with chromatic number 5.
(4 Marks)
Question 4:        
                                                                                                               
(a) Solve following recurrence relations                                   (9 Marks)          
                   
i) =  + n,  = 2            
       using substitution method
ii) 9
iii) =
(b) Write a short note on  Tower  of  Hanoi  Problem.  How can it be
solved using recursion ? (4 Marks)
Question 5:
(a) Show that for subgraph H of a graph G                                             (4 Marks)
                            ∆ (H) ≤ ∆ (G)
(b) What is Divide and Concuer relations? Explain  with an example?       (4 Marks)
(c)  Find a power series associated with the problem  where we have to
find a number of ways to select 10 people to form and expert committee
from 6 Professors and 12 Associate Professors.  (4 Marks)
(d) Tree is a Bipartite Graph” justify the statement with an example?   (4 Marks)

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