MCS033 Advance Discrete Mathematics Solved assignment 2018-19

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Advanced Discrete Mathematics Solved 

Question 1:  Give an example of a second order linear homogenous recurrence relation with constant coefficients.   
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?
                       (i) 𝑓n = 𝑓n-1 + 𝑓n-2
                       (ii) 𝑎n =5𝑎n-1 + 𝑛3
                       (iii) 𝑎n =𝑎n-1 + 𝑎n-2 +…. 𝑎0
                       (iv) 𝑎n = 5𝑎n-1 𝑎n-2
Question (b): Solve the following recurrences relation
                           i)   𝑆n = 2𝑆n-1       
                          ii) Find an explicit recurrence relation for minimum number of moves in which the 𝑛-disks in tower of Hanoi puzzle can be solved! Also solve the obtained recurrence relation through an iterative method.         
Question 2: Draw 2-isomorphic graphs and 3 non- isomorphic graphs on five vertices.   
Question 3: Prove that the complement of 𝐺 is 𝐺   
Question 4: Find λ(𝐺), when 𝐺 is a Peterson graph.
Question 5: Write the expression for a linear homogenous recurrence relation with constant coefficients of degree 𝐾 and explain the basic approach to solve it.                                   
Question 6: Draw the following graphs and state which of following graph is a regular graph?
                    (i) 𝐶5 (ii) 𝑊5  (iii) 𝑄4  (iv) 𝐾5,5 (v) 𝐾5 
Question 7 (a): What is a chromatic number of a graph?               
 (b) Determine whether the above graph has a Hamiltonian circuit. If it has,     find such a circuit. If it does not have, justify it 
Question 8 (a): What is the solution of the following recurrences relation          an  = an-1 + 2an-1,  n > 2      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 
Question 10: Determine the number of subsets of a set of n element, where n > 0   
Question 11: Show that K5 is not a planar graph.



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