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What do you understand by a subdivision of a graph? Is every subdivision of a Hamiltonian graph Hamiltonian? Justify.
Solve the recurrence relation:
Draw three nonisomorphic induced subgraphs of the following graph, each having the same number of vertices. Justify your choice.
Solve the recurrence relation:
using generating function technique. Also find 5 a using your answer.
Is there a 4-regular graph on 7 vertices? Justify your answer.
Check whether the following statements are true or not. Justify your answers with a short proof or a counter example
i) If the contrapositive of a statement is true, then the statement itself is also true.
ii) is a linear homogeneous recurrence relation.
iii) A particular solution of the recurrence relationhas the form
iv) There exists a boolean expression in variables
v) If a dice is rolled thrice, then the probability of getting a 6 each time is
vi) Every odd cycle has the same chromatic and edge chromatic numbers.
vii) Every Eulerian graph is Hamiltonian.
viii) 3 4 S gives the number of ways in which any 3 objects can be placed in any 4 boxes.
ix) There exists a self-complementary planar graph on 5 or more vertices.
x) The number of partitions of 6 is 10.
Express the following statements in symbolic form.
i) There is a man in the park with blue eyes.
ii) Every blue-eyed man in the park is wearing a red hat.
iii) If a man wears no hat, then he has black eyes