Which of the following statements is true about Eulerian paths ?Select one:a. Every connected graph has an Eulerian path.b. An Eulerian path exists if and only if every vertex in the graph has an odd degree.c. An Eulerian path can exist even if the graph is not connected.d. An Eulerian path exists in a connected graph if and only if exactly zero or two vertices have odd degrees.

The correct answer is:

d. An Eulerian path exists in a connected graph if and only if exactly zero or two vertices have odd degrees.

Here's why:

a. Not every connected graph has an Eulerian path. For example, a simple graph with 3 vertices and 3 edges (forming a triangle) does not have an Eulerian path.

b. An Eulerian path does not exist if and only if every vertex in the graph has an odd degree. In fact, an Eulerian path exists if and only if exactly zero or two vertices have odd degrees.

c. An Eulerian path cannot exist if the graph is not connected. This is because an Eulerian path is a path in a graph which visits every edge exactly once. If the graph is not connected, there will be edges that cannot be reached and therefore cannot be included in the path.

d. An Eulerian path exists in a connected graph if and only if exactly zero or two vertices have odd degrees. This is the correct statement. If all vertices have even degrees, we have an Eulerian cycle (which is a special case of an Eulerian path). If exactly two vertices have odd degrees, we have an Eulerian path starting at one of them and ending at the other.