Pascal’s Formula

What is isomorphism? Find, if the following graphs G1 and G2 are isomorphic or not. Explain how you arrived at your answer.

Prove the following theorem by direct proof method: ‘‘The square of an even integer is an even integer.’’

Travelling Salesman Problem

Show, using the pigeonhole principle, that in any group of 30 people, 5 people can always be found who were born on the same day of the week.

Path

How Hamiltonian graphs differ from the Eulerian graphs? Give Dirac’s and Ore’s criterion for the Hamiltonian graphs.