Question

use the graph to determine whether the path described is an euler path, an euler circuit, or neither. explain your answer. a, b, c, d, e, f, b, e, c choose the correct answer below. a. the path described is an euler circuit because it is an euler path that begins and ends at the different vertices. b. the path described is neither an euler path nor an euler circuit because at least one edge is traveled more than once. c. the path described is an euler path because every edge is traveled exactly once. 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 vertex 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 travels every edge exactly once. An Euler circuit is an Euler path that starts and ends at the same vertex.
In the given path \(A,B,C,D,E,F,B,E,C\), we can check the edges:

• For example, the edge \(BE\) is traversed twice (once from \(E\) to \(B\) and once from \(B\) to \(E\)). So not every edge is traversed exactly once.

Answer:

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