In question nothing is mentioned so it may be connected or not connected ( components >2)
if take not connected ( components=2)
one component is triangle ( regular graph with degree 2 ( even degree))
second component is 2 vertices and 1 edge ( both vetex have degree 1 ( odd degree))
now node V added to both vetex of second component so second component become regular graph with degree 2
Hence resultant graph is regular.
but this is not possible with every case .
For complete,Hamiltonian,Euler graph , graph should be connected then how these graph are possible with disconnected graph
Therefore if we consider graph as disconnected then no option match as answer
Plz verify this