Question

explain why the graph shown to the right has no euler paths and no euler circuits.

choose the correct answer below.

a. by eulers theorem, the graph has no euler paths and no euler circuits because it has exactly two odd vertices.

b. by eulers theorem, the graph has no euler paths and no euler circuits because it has more than two odd vertices.

c. by eulers theorem, the graph has no euler paths and no euler circuits because it has all even vertices.

d. by eulers theorem, the graph has no euler paths and no euler circuits because it has an even number of odd vertices.

Explanation:

Euler's Theorem states that a graph has an Euler circuit if all vertices are even - degree. A graph has an Euler path if it has exactly two odd - degree vertices. If a graph has more than two odd - degree vertices, it has neither an Euler circuit nor an Euler path.

Answer:

B. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has more than two odd vertices.