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Automorphism group of the complete transposition graph
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ganesan, Ashwin |
| Copyright Year | 2015 |
| Abstract | The complete transposition graph is defined to be the graph whose vertices are the elements of the symmetric group Sn, and two vertices α and β are adjacent in this graph iff there is some transposition (i, j) such that α = (i, j)β. Thus, the complete transposition graph is the Cayley graph Cay(Sn, S) of the symmetric group generated by the set S of all transpositions. An open problem in the literature is to determine which Cayley graphs are normal. It was shown recently that the Cayley graph generated by 4 cyclically adjacent transpositions is non-normal. In the present paper, it is proved that the complete transposition graph is not a normal Cayley graph, for all n ≥ 3. Furthermore, the automorphism group of the complete transposition graph is shown to equal Aut(Cay(Sn, S)) = (R(Sn) o Inn(Sn)) o Z2, where R(Sn) is the right regular representation of Sn, Inn(Sn) is the group of inner automorphisms of Sn, and Z2 = 〈h〉, where h is the map α 7→ α−1. Index terms — complete transposition graph; automorphisms of graphs; normal Cayley graphs. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://84f43698-a-62cb3a1a-s-sites.googlegroups.com/site/ashwinganesan/JACOfinalversion.pdf?attachauth=ANoY7crOJXUcv1eWeB44LGjWDdz7BuDMlyu4aWOX0OG597f1UhN6MxfVkgeJ81ASx2SPAzfPa2POEecHGmg8hTPNbzElk-Tf-RIIrf7msZdzgXiNS8Mpr6GmEauuVEvFZiG2jJXEyVA-VqTFBUtbvIBl1aw97lG6SFZoJvwUYmmkkY1gl7pN83G48g3BVluZM9vZcRJMdKMk--Q3aGEuicCGHlwADXkWMMGN8LTNgfqaRr5ZTK7VNx8%3D&attredirects=1 |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Graph - visual representation Graph automorphism Magma Vertex (geometry) |
| Content Type | Text |
| Resource Type | Article |
