Consider the following graphs Which of these have an Euler c

Consider the following graphs Which of these have an Euler circuit? Graph (i), Graph (ii), Graph (iii) Circle all that are correct. For those that do indicate an Euler circuit by listing the vertices in the order used. Which of these have a Hamilton circuit? Graph (i), Graph (ii), Graph (iii) Circle all that are correct For those that do indicate a Hamilton circuit by listing the vertices in the order used.

Solution

a) Only graph 3 has an Euler circuit.

Circuit is A-D-B-E-H-G-E-D-C-G-F-C-A.

b)Graph i has an Hamiltonian path.

A-B-D-C-E.

Graph III also has an Hamiltonian path.

A-C-F-G-H-E-D-B

(since these visit all vertices exactly once)

But no graph has hamiltonian circuit.