From the description it is clear that vertices are connected as follows:
$1-9-17-...-97$
$2-10-18-...-98$
$3-11-19-...-99$
$4-12-20-...-100$
$5-13-21-...-93$
$6-14-22-...-94$
$7-15-23-...-95$
$8-16-24-...-96$
We have covered all vertices using $8$ vertex sets considering only $\mid i - j \mid = 8$. Using $\mid i - j \mid = 12$ we can see the vertex $1$ is connected to $13, 2-14, 3-15$ and $4-16$, so the top $4$ vertex sets are in fact connected to the bottom $4$ sets, thus reducing the connected components to $4$.
Correct Answer: $B$