Geodesic
Characterization of simple orbit graphs
Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 2 
A.  Bretto; A. Faisant; C. Jaulin; J. Tomanová. Characterization of simple orbit graphs. Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2010_79_2_a2/
@article{AMUC_2010_79_2_a2,
     author = {A.  Bretto and A. Faisant and C. Jaulin and J. Tomanov\'a},
     title = {Characterization of simple orbit graphs},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2010},
     volume = {79},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2010_79_2_a2/}
}
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Let G be a (finite) group and let S be a non-empty subset of G . The vertex set of the orbit graph O(G,S) is the collection, over all s Î S , of orbits of left translations induced by s . If u and v are distinct vertices (each representing an orbit of some s and t from S ), then for any gÎ G appearing in both orbits there is an edge colored g in O ( G,S ) joining u and v . Orbit graphs are an important special case of " G -graphs" introduced by Bretto and Faisant in Math. Slovaca 55 (2005). In this paper we characterize simple orbit graphs and apply the result to show that certain class of simple orbit graphs is closed under the construction of incidence graphs.