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On the Automorphism Groups of Cayley Graphs of Finite Simple Groups |
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| Authors: | Fang, Xin Gui Praeger, Cheryl E. Wang, Jie |
| Affiliation: | Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University Beijing 100871, China, xgfang{at}sxx0.math.pku.edu.cn Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University Beijing 100871, China, wangj{at}pku.edu.cn Department of Mathematics and Statistics, University of Western Australia 35 Stirling Highway, Crawley, WA 6009, Australia, praeger{at}maths.uwa.edu.au |
| Abstract: | Let G be a finite nonabelian simple group and let  be a connectedundirected Cayley graph for G. The possible structures for thefull automorphism group Aut are specified. Then, for certainfinite simple groups G, a sufficient condition is given underwhich G is a normal subgroup of Aut. Finally, as an applicationof these results, several new half-transitive graphs are constructed.Some of these involve the sporadic simple groups G = J1, J4,Ly and BM, while others fall into two infinite families andinvolve the Ree simple groups and alternating groups. The twoinfinite families contain examples of half-transitive graphsof arbitrarily large valency. |
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