For the following graph of G is there an Euler circuit If so

For the following graph of G, is there an Euler circuit? If so, give one. If not, explain why. An Euler path that is not a circuit? If so, give one. If not, explain why. A Hamilton circuit? If so, give one. Of not, explain why.

Solution

a) No, Euler circuit because there are vertices {b,f} which have odd number of edges.

b) Yes, because exactly 2 verices have odd number of edges therefore the Euler path is (f-a-b-c-d-i-h-g-f-e-h-d-e-b)

c) No there is not any Hamiltonian circuit for the given graph because of the vertex e.

d) Yes there is Hamiltonian path (f-a-b-c-d-i-h-g-f-e-h-d-e-b) because it covers all the edges once.