On the genus of the star graph
نویسنده
چکیده
The star graph S n is a graph with S n the set of all permutations over f1; : : :; ng as its vertex set; two vertices 1 and 2 are connected if 1 can be obtained form 2 by swapping the rst element of 1 with one of the other n ? 1 elements. In this paper we establish the genus of the star graph. We show that the genus, g n of S n , 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.
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