%0 Journal Article %1 behrendt:1990 %A Behrendt, G. %D 1990 %I Wiley Subscription Services, Inc., A Wiley Company %J Journal of Graph Theory %K automorphismgroup picture %N 4 %P 423--426 %R 10.1002/jgt.3190140405 %T Automorphism groups of pictures %U http://dx.doi.org/10.1002/jgt.3190140405 %V 14 %X Abstract A picture is a simple graph together with an edge-coloring, such that each vertex is incident with exactly one edge of each color. An automorphism of a picture is a graph automorphism that preserves the colors of the edges. We show that every group is isomorphic to the full automorphism group of a picture, and prove that a group is isomorphic to a vertex-transitive subgroup of the automorphism group of a picture if and only if it can be generated by involutions.

@article{behrendt:1990, abstract = {Abstract A picture is a simple graph together with an edge-coloring, such that each vertex is incident with exactly one edge of each color. An automorphism of a picture is a graph automorphism that preserves the colors of the edges. We show that every group is isomorphic to the full automorphism group of a picture, and prove that a group is isomorphic to a vertex-transitive subgroup of the automorphism group of a picture if and only if it can be generated by involutions.}, added-at = {2011-08-19T11:33:43.000+0200}, author = {Behrendt, G.}, biburl = {https://www.bibsonomy.org/bibtex/247fefabcd448a0fa49e02dbccd36a6a3/ulpsch}, doi = {10.1002/jgt.3190140405}, interhash = {19f3909aef46c24fa4998cb1c07c6de9}, intrahash = {47fefabcd448a0fa49e02dbccd36a6a3}, issn = {1097-0118}, journal = {Journal of Graph Theory}, keywords = {automorphismgroup picture}, number = 4, pages = {423--426}, publisher = {Wiley Subscription Services, Inc., A Wiley Company}, timestamp = {2012-01-16T16:21:42.000+0100}, title = {Automorphism groups of pictures}, url = {http://dx.doi.org/10.1002/jgt.3190140405}, volume = 14, year = 1990 }