## Description

**Course Code : MCS-033**

**Course Title : Advanced Discrete Mathematics**

**Assignment Number : MCA(III)/033/Assignment/2018-19**

**Maximum Marks : 100**

**Weightage : 25%**

**Last Dates for Submission : 15th October, 2018 (For July session)**

**15th April, 2019 (For January session)**

**This assignment has eleven questions, which carries 80 marks. Answer all the**

**questions. The rest 20 marks are for viva voce. You may use illustrations. Place**

**go through the guidelines regarding assignments given in the Programme Guide**

**for the format of presentation.**

Question 1: Give an example of a second order linear homogenous recurrence

relation with constant coefficients. (2 Marks)

Question (a): Find the order and degree of the following recurrences relation|. Which

of the following belongs to the linear homogenous recurrence relation

with constant coefficient? (8 Marks)

(i) ?n = ?n-1 + ?n-2

(ii) ?n =5?n-1 + ?

3

(iii) ?n =?n-1 + ?n-2 +…. ?0

(iv) ?n = 5?n-1 ?n-2

Question (b): Solve the following recurrences relation

i) ?n = 2?n-1 (5 Marks)

ii) Find an explicit recurrence relation for minimum number of moves in

which the ?-disks in tower of Hanoi puzzle can be solved! Also solve

the obtained recurrence relation through an iterative method.

(5 Marks)

Question 2: Draw 2-isomorphic graphs and 3 non- isomorphic graphs on five

vertices. (5 Marks)

Question 3: Prove that the complement of ? is ? (5 Marks)

Question 4: Find λ(?), when ? is a Peterson graph (5 Marks)

Question 5: Write the expression for a linear homogenous recurrence relation with

constant coefficients of degree ? and explain the basic approach to solve

it. (5 Marks)

7

Question 6: Draw the following graphs and state which of following graph is a

regular graph? (5 Marks)

(i) ?5 (ii) ?5 (iii) ?4 (iv) ?5,5 (v) ?5

Question 7 (a): What is a chromatic number of a graph? What is a chromatic number

of the following graph? (5 Marks)

(b) Determine whether the above graph has a Hamiltonian circuit. If it has,

find such a circuit. If it does not have, justify it (5 Marks)

Question 8 (a): What is the solution of the following recurrences relation

an = an-1 + 2an-1, n > 2 (10 Marks)

with a0 = 0, a1=1

(b) an =2n

an-1, n > 0 with initial condition a0 =1

Question 9: Show that if G1, G2 …. Gn are bipartite graph UG is a bipartite graph

(5 Marks)

Question 10: Determine the number of subsets of a set of n element, where n > 0

(5 Marks)

Question 11: Show that K5 is not a planar graph.

MCS-033, MCS-33, MCS 033, MCS 33, MCS033, MCS33, MCS

## Reviews

There are no reviews yet.