Problem 4.1 : Determine whether the graph shown on the right has an Euler circuit or an Euler path. Choose the correct answer below.
(A) The graph has an Euler circuit.
(B) The graph has an Euler path.
(C) The graph has both an Euler circuit and an Euler path.
(D) The graph has neither an Euler circuit nor an Euler path.
(E) There is not enough information to be sure.
Explain you reasoning, by choosing the correct answer below:
(A) All the vertices are odd.
(B) All the vertices are even.
(C) The graph has more than two odd vertices.
(D) The graph has more than two even vertices.
(E) The graph may or may not be connected.
Problem 4.2 : Determine whether a graph that has 7 vertices, all of degree 6, has an Euler circuit or an Euler path. Choose the correct answer below.
(A) The graph has an Euler circuit.
(B) The graph has an Euler path.
(C) The graph may or may not have an Euler circuit
(D) The graph has neither an Euler circuit nor an Euler path.
(E) The graph may or may not have an Euler path.
Explain you reasoning, by choosing the correct answer below:
(A) All the vertices are odd.
(B) All the vertices are even.
(C) The graph has more than two odd vertices.
(D) The graph has more than two even vertices.
(E) The graph may or may not be connected.