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A New Upper Bound for the Diameter of the Cayley Graph of a Symmetric Group
Zhuang, Hangwei
Zhuang, Hangwei
Abstract
Given a finite symmetric group S_n and a set S of generators, we can represent the group as a Cayley graph. The diameter of the Cayley graph is the largest distance from the identity to any other elements. We work on the conjecture that the diameter of the Cayley graph of a finite symmetric group S_n with S ={(12),(12...n)} is at most $ C(n,2). Our main result is to show that the diameter of the graph of S_n is at most (3n^2-4n)/2.
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2018-05-01
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Mathematics