Question

use the graph to determine whether the path described is an euler path, an euler circuit, or neither. explain your answer.
a, b, e, f, b, c, d, e, c

choose the correct answer below
a. the path described is neither an euler path nor an euler circuit because at least one edge is traveled more than once.
b. the path described is an euler path because every vertex is traveled exactly once.
c. the path described is an euler circuit because it is an euler path that begins and ends at the different vertices.
d. the path described is neither an euler path nor an euler circuit because not every edge is traveled once.
e. the path described is an euler path because every edge is traveled exactly once.
f. the path described is an euler circuit because it is an euler path that begins and ends at the same vertex.

Explanation:

An Euler path is a path that uses every edge of a graph exactly once. An Euler circuit is an Euler path that starts and ends at the same vertex. In the given path \( ABEFBCDEC \), the edge \( BC \) is traversed more than once. Since an Euler path (and thus an Euler circuit) requires each edge to be used exactly once, this path fails that requirement.

Answer:

A. The path described is neither an Euler path nor an Euler circuit because at least one edge is traveled more than once.