option D should be wrong, and Option C should be right !
Option C if graph is disconnected then there is no path ib between 1 And N .
graph may be disconnected., But the nth vertex should be connected to the component which is the 1st vertex is connected !
let there are r components.... let the 1st vertex connected component is C1.
We all know that each component is a sub-graph, means it is also a graph.
therefore C1 is also a graph... 1st vertex is odd degree vertex, then there should be exist one more odd degree ( in worst case ) ===> all vertices have 4 as degree ===> nth vertex should be connected to C1 only.
Therefore a path should be exist between them.
if you didn't get this try to draw a graph without nth vertex connecting to C1.