I-graphs and the Corresponding Configurations

We consider the class of I-graphs I(n, j, k), which is a generalization over the class of the generalized Petersen graphs. We study different properties of I-graphs such as connectedness, girth and whether they are bipartite or vertex-transitive. We give an efficient test for isomorphism of I-graphs and characterize the automorphism groups of I-graphs. Regular bipartite graphs with girth at least 6 can be considered as Levi graphs of some symmetric combinatorial configurations. We consider configurations which arise from bipartite I-graphs. Some of them can be realized in the plane as cyclic astral configurations, i.e. as geometric configurations with maximal isometric symmetry.