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Posted Date: 25 Nov 2008 Posted By: Arun Kumar Saanam Member Level: Gold
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2008 Andhra Pradesh State Jawaharlal Nehru Technological University B.Tech DISCRETE STRUCTURES AND GRAPH THEORY [Set No 1] Question paper
Code No: RR210501 Set No. 1
II B.Tech I Semester Supplimentary Examinations, February 2008
DISCRETE STRUCTURES AND GRAPH THEORY
( Common to Computer Science & Engineering, Information Technology,
Computer Science & Systems Engineering and Electronics & Computer
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Show that RVS follows logically from premises. [8+8]
C_D, (C _ D) !? H,? H ! (A ^? B) (A ^? B) ! R _ S
(b) Show that R ! S can be derived from the premises P!(Q! S), ? R_P and
Q.
2. (a) What are the properties of the relation r = ( i, j ) / |i - j| = 2 on the set
A = { 1, 2, 3, 4, 5, 6 }. [8+8]
(b) Determine all the bijections from { 1, 2, 3 } on to {a, b, c, d}.
3. (a) Define the term ‘lattice’, clearly stating the axioms. [6]
(b) Let C be a collection of sets which are closed under intersection and union.
Verify whether (C, \, [) is a lattice. [10]
4. (a) Prove that any two simple connected graphs with n vertices and all of degree
two are isomorphic [8+8]
(b) Suppose G1 and G2 are isomorphic prove that if G1 is connected then G2 is
also connected.
5. (a) Prove that the Kuratowskis second graph consisting of 6 vertices and 9 edges
is non-planar.
(b) State criteria to detect the planarity of a connected graph and give an example
also. [8+8]
6. (a) Write a detailed algorithm for depth-first traversal using an adjacency matrix
that just prints the node label as the visit operation. You should trace it using
the graphs. [8+8]
(b) Prove that each edge in a connected graph will be part of the depth-first
traversal tree or will be an edge pointing to a predecessor in the tree.
7. (a) How many integral solutions are there of x1 + x2 + x3 + x4 + x5 = 30 where
for each; [10]
i. xi 0;
ii. xi 1;
iii. x1 2, x2 3, x3 4, x4 2, x5 0;
iv. xi i.
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Code No: RR210501 Set No. 1
(b) Six distinct symbols are transmitted through a communication channel. A
total of 12 blanks are to be inserted between the symbols with at least 2
blanks between every pair of symbols. In how many ways can the symbols
and blanks be arranged? [6]
8. (a) Explain the properties of Fibonacci Numbers. [8+8]
(b) Find a recurrence relation for the number of ways to make a pile of n chips
using garnet, gold, red, white and blue chips such that no two gold chips are
together.
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