Abstract
The star graph Sn is a graph with Sn the set of all permutations over {1,...,n} as its vertex set; two vertices π1 and π2 are connected if π1 can be obtained form π2 by swapping the first element of π1 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