If you are on this Page You Want to Download IGNOU MCS 033 Important Questions 2021 Advanced Discrete Mathematics. In this section, You will find all the Exam important Questions of all courses which are divided by the Section “SEMESTER WISE”.
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| S.NO | Important Questions Of Try to Solve These Questions |
| 1 | (a) What is generating function ? Define exponential generating function. (b) Is every subgraph of a regular graph, regular ? Give reasons for your answer |
| 2 | (a) What is bipartite graph ? What is the chromatic number of any bipartite graph ? Show that C6 is a bipartite and K3 is not a bipartite graph. (b) Draw at least two non-isomorphic graphs on four vertices. |
| 3 | (a) Construct a non-Hamiltonian graph on five vertices. |
| 4 | (a)Let G be a graph with n vertices. Prove that the following statements are equivalent : (i) G has no cycles and (n – 1) edges. (ii) Any two vertices of G are connected by exactly one path. |
| 5 | (a) A software company offers an initial annual salary of < 3,00,000 and an annual increment of 25% of previous year’s salary. Find the recurrence relation for the salary at the beginning of the nth year. |
| 6 | (a)Prove that the sum of the degree of vertices of any graph is twice the number of edges |
| 7 | (a)State the Tower of Hanoi problem. Write its recurrence relation and explain its formulation. |
| 8 | (a) Explain the steps required to solve the linear homogeneous recurrence relation with constant coefficients through characteristic equation. (b) What are generating functions ? Why are they used ? |
| 9 | (a) Find the generating function for finite sequence : 2, 2, 2, 2, 2, 2 (b) Draw a 5-regular graph on 10 vertices |
| 10 | (a)Consider the following two degree sequence of any graph. Determine, for which sequence graph is possible, if not explain why ? (i) (3, 2, 2, 2, 1) (ii) (3, 2, 2, 2, 1, 1) |
| 11 | Prove that a connected graph G with two or more vertices is edge traceable if and only if it has exactly two vertices of odd degree. |
| 12 | Find the generating function for the following sequence 1, 1, 1, 1, 1, 1, 0, 0, O. |
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