Question 1 (8 Marks, 2015 Exam)

Define an isomorphism of graphs. Which of the following graphs are isomorphic? Justify your answer.

Question 2 (10 Marks)

a) Define what it means for a graph to be Eulerian, semi-Eulerian, Hamiltonian, and semi-Hamiltonian.

b) Give an example of a graph with 5 vertices such that \(G\) is Hamiltonian but not semi-Eulerian. Justify that \(G\) has these properties.

c) Give an example of a graph with 5 vertices such that \(G\) is Eulerian but not semi-Hamiltonian. Justify that \(H\) has these properties.

Question 3 (7 Marks)

Given that Fluorine (\(F\)) has valency 1, prove that any molecule with formula \(C_5H_{11}F\) is a tree. How many isomers does \(C_5H_{11}F\) have? Draw them.