The star graph Sn is a graph with Sn the set of all permutations over f1; : : : ; ng as
its vertex set; two vertices ss1 and ss2 are connected if ss1 can be obtained form ss2 by
swapping the first element of ss1 with one of the other n ? 1 elements. In this paper
we establish the genus of the star graph. We show that the genus, gn of Sn , is exactly
equal to n!(n?4)=6+1 by establishing a lower bound and inductively giving a drawing
on a surface of appropriate genus.