option B is the right answer
We can solve this question by eliminating options
Option (A) False
Let us take a complete graph of $4$ vertices:
In a line graph, no. of edges is
$\sum_{i=0}^{n}$ ${}^{d_{i}}C_{{2}},$ $d_{i}$is degree of each vertex
=$\frac{3\times 2}{2}+\frac{3\times 2}{2}+\frac{3\times 2}{2}+\frac{3\times 2}{2} = 3\times 4=12$
No. of vertices in line graph = No. of edges in original graph
No. of vertices in line graph $= 6$
So, no. of edges to make complete graph with $6$ vertices $= \frac{6\times 5}{2} = 3\times 5=15$
But for given line graph from complete graph of $4$ vertices we have only $12$ edges.
Contradiction.
Option (B) True
1. Smallest line graph for original graph one edge
which is also connected graph
If a graph is connected with more then one edge, it will never be disconnected
Option (C) False
This cannot be 2-colorable and hence is not bipartite.
Option (D) False
Because line graph degree of vertex depends on the attribute
e.g., $\left [ A,B \right ]$ as point in line graph, then degree of this vertex depends on degree of $A$ and degree of $B$ in the original graph.
I'm drawing degree for a point $[AB]$ in line graph.
So, this is wrong.
Option (E) False (wrong as proved in above option (D))