$1.($A$)$ Consider the graph $7$ with vertices $\{0,1,2,...,6\}$ and where

two vertices are joined by an edge if and only if their indices differ by $2$

mod $7.($Notice$,$ for instance, that $5$ is joined to $0$ by this rule.$)$ Draw

this graph.

$($B$)$ Repeat exercise $($A$)$ for the graph $8$ with vertices $\{0,1,...,7\}$

and where two vertices are joined by an edge if and only if they differ

by $2$ mod $8.$

$($C$)$ Comment on any structural similarities and$/$or differences you

notice in the graphs $7$ and $$