The necessary and sufficient condition for a graph to be Eulerian is:a.All vertices have even degreeb.All vertices have odd degreec.All vertices have the same degreed.There is a path between every pair of vertices

The necessary and sufficient condition for a graph to be Eulerian is that all vertices have even degree.

The necessary and sufficient condition for a graph to be Eulerian is: a. All vertices have even degree.

An Eulerian graph is a graph in which all vertices have an even degree. This means that every vertex has an equal number of incoming and outgoing edges. This allows for a continuous path to be drawn through the graph that visits every edge exactly once, which is the definition of an Eulerian path.

Here are the steps to determine if a graph is Eulerian:

1. Identify the degree of each vertex in the graph. The degree of a vertex is the number of edges that connect to it.

2. Check if all vertices have an even degree. If they do, the graph is Eulerian. If any vertex has an odd degree, the graph is not Eulerian.

Note: The condition "There is a path between every pair of vertices" is not necessary for a graph to be Eulerian. However, it is necessary for a graph to be connected, which is a different property.