Let $G$ be a graph of order $n$ in which every vertex has degree equal to $d$. How large must $d$ be in order to guarantee that $G$ is connected?
in this question, you have to take care of odd and even number of vertices also !
So, more precisely option B is right !
For a graph with 2 vertices, the number of edges is 1 and degree of each edge is 1.
Value of option A, B, C = 1
Value of option D = 1/2
So D cannot be the answer.
For a graph with 3 vertices and 3 edges, degree of each vertex is 2.
Value of option A, B = 1
Value of option C = 2
So A and B cannot be the answer.
Therefore C should the answer.
(My answer doesn't match with the given solution, but I arrived at this conclusion by eliminating the options.)