Counter example for

A,B,C-- cycle of 3 vertices. n=3,d=2

D-- cycle of 4 vertices. n=4,d=2.

Now assume that option e is false.

I.e.,both n,d are odd. I.e there are odd number of vertices with odd degree... Which is violating the property of graph that "there are even number of vertices of odd degree in a graph"

Hence our assumption is false and option E is true.

A,B,C-- cycle of 3 vertices. n=3,d=2

D-- cycle of 4 vertices. n=4,d=2.

Now assume that option e is false.

I.e.,both n,d are odd. I.e there are odd number of vertices with odd degree... Which is violating the property of graph that "there are even number of vertices of odd degree in a graph"

Hence our assumption is false and option E is true.