%0 Journal Article %1 springerlink:10.1007/BF02579330 %A Godsil, C. %D 1981 %I Springer Berlin / Heidelberg %J Combinatorica %K Cayley-Graphen Automorphismen Graphen %P 243-256 %T On the full automorphism group of a graph %U http://dx.doi.org/10.1007/BF02579330 %V 1 %X While it is easy to characterize the graphs on which a given transitive permutation groupG acts, it is very difficult to characterize the graphsX with Aut (X)=G. We prove here that for the certain transitive permutation groups a simple necessary condition is also sufficient. As a corollary we find that, whenG is ap-group with no homomorphism ontoZ p wrZ p , almost all Cayley graphs ofG have automorphism group isomorphic toG.

@article{springerlink:10.1007/BF02579330, abstract = {While it is easy to characterize the graphs on which a given transitive permutation groupG acts, it is very difficult to characterize the graphsX with Aut (X)=G. We prove here that for the certain transitive permutation groups a simple necessary condition is also sufficient. As a corollary we find that, whenG is ap-group with no homomorphism ontoZ p wrZ p , almost all Cayley graphs ofG have automorphism group isomorphic toG.}, added-at = {2013-02-02T14:41:54.000+0100}, affiliation = {Institut f{\"u}r Mathematik und Angewandte Geometrie Mountanuniversit{\"a}t Leoben Austria Mountanuniversit{\"a}t Leoben Austria}, author = {Godsil, C.}, bdsk-file-1 = {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}, bdsk-url-1 = {http://dx.doi.org/10.1007/BF02579330}, biburl = {https://www.bibsonomy.org/bibtex/2a1536acc73a12c38aa12f13131fe18fb/ks-plugin-devel}, date-added = {2011-04-26 10:59:23 +0200}, date-modified = {2011-04-26 10:59:47 +0200}, file = {:Godsil/On the full automorphism group of a graph.pdf:PDF}, groups = {public}, interhash = {f58bf124ed50908547b055827d8cd3f0}, intrahash = {a1536acc73a12c38aa12f13131fe18fb}, issn = {0209-9683}, issue = {3}, journal = {Combinatorica}, keyword = {Mathematics and Statistics}, keywords = {Cayley-Graphen Automorphismen Graphen}, note = {10.1007/BF02579330}, pages = {243-256}, publisher = {Springer Berlin / Heidelberg}, timestamp = {2013-02-02T14:41:54.000+0100}, title = {On the full automorphism group of a graph}, url = {http://dx.doi.org/10.1007/BF02579330}, username = {keinstein}, volume = 1, year = 1981 }