$3.(12$ points$)$ Define the graph $\backslash ($ G$\_\{$n$\}\backslash )$ to be the directed graph with $\backslash ($ n $\backslash )$ vertices each labeled a different integer from $\backslash (1,2,\backslash$ldots$,$ n $\backslash ).$

There is a directed edge from vertex $\backslash ($ i $\backslash )$ to vertex $\backslash ($ j $\backslash )$ if $\backslash (0$