Discrete structures
Previous year question paper with solutions for Discrete structures
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- Prove that an undirected graph has an even number of vertices of odd degree
- Define the terms (i) Hamilton Path (ii) Hamilton Cycle
- Define a planar graph and give an example of a non-planar graph
- Define a rooted tree
- Define a partial order relation and give an example of the same.
- If (ab) = a 2 b 2 a,b G, where G is a group, then show that G is commutative.
- a,b R where R is a ring , show that a.0 = 0
- Give an example of an infinite integral domain.
- In a Boolean algebra B, show that, a + l = 1aB
- What is the generating function for the sequence 1!nSn ?
- If H is a subgroup of the group G, among the right cosets of H in G, prove that ther is only one subgroup, viz. H
- Let f : X X;X = {0,1,2,3,4,5,6} defined by f (x) = 4x mod 5. Write the function f as a set of ordered pairs.
- Give an example of Hamiltonian graph
- Define semigroup.
- Find the number of distinct permutations that can be formed from all the letters of the word ‘MATHEMATICS’
- Show that the set of 2 × 2 non-singular matrices with rational entries is a group with respect to matrix multiplication.
- Let D70 = {1, 2, 5, 7, 10, 14, 35, 70} and define m n, if m divides n. Show that (D70, ) is a Boolean Algebra.
- Define chromatic number.
- What is the difference between a graph and a tree?
- If P(n, r) = 0, then what is the value of r?
- What do you mean by principle of inclusion-Exclusion?
- Is every function is a relation? Comment on it and explain your answer
- Determine whether the following function is a bijection from R to R. f(x) = - 3x2 + 7
- Determine whether the relation R on the set of nil people is reflexive, symmetric and/or transitive, where (a,b) ∈ R if and only if a is taller than b
- Prove that an undirected graph has an even number of vertices of odd degree.
- What do you mean by Euler Circuit? Explain with example
- Is K3,3 is a planar Graph? Explain your answer. Here K3,3 represent a Bipartite graph.
- Prove the absorption law x(x + y) = x using the other identities of Boolean algebra
- What is chromatic number of Kn graph (Complete Graph).
- Define monoid.