1. The Möbius-Kantor graph is a faithful unit-distance graphNino Bašić, Gábor Gévay, Tomaž Pisanski, 2026, original scientific article Abstract: In this paper, it has been shown that the generalized Petersen graph GP(8, 3), also known as the Möbius-Kantor graph, admits a faithful unit-distance representation in the plane.
Keywords: polycirculant, unit-distance graph, Möbius–Kantor graph, generalized Petersen graph
Published in RUP: 08.09.2026; Views: 357; Downloads: 0 |
2. Polycyclic geometric realizations of the Gray configurationLeah Berman, Gábor Gévay, Tomaž Pisanski, 2025, original scientific article Abstract: The Gray configuration is a (27_3) configuration which typically is realized as the points and lines of the 3×3×3 integer lattice. It occurs as a member of an infinite family of configurations defined by Bouwer in 1972. Since their discovery, both the Gray configuration and its Levi graph (i.e., its point-line incidence graph) have been the subject of intensive study. Its automorphism group contains cyclic subgroups isomorphic to Z3 and Z9, so it is natural to ask whether the Gray configuration can be realized in the plane with any of the corresponding rotational symmetry. In this paper, we show that there are two distinct polycyclic realizations with Z3 symmetry. In contrast, the only geometric polycyclic realization with straight lines and Z9 symmetry is only a “weak” realization, with extra unwanted incidences (in particular, the realization is actually a (27_4) configuration).
Keywords: Gray graph, Gray configuration, polycirculant, polycyclic configuration
Published in RUP: 29.09.2025; Views: 1120; Downloads: 7
 Full text (2,95 MB) |
3. The Gray graph is a unit-distance graphLeah Berman, Gábor Gévay, Tomaž Pisanski, 2025, original scientific article Abstract: In this note we give a construction proving that the Gray graph, which is the smallestcubic semisymmetric graph, is a unit-distance graph.
Keywords: polycirculant, unit-distance graph, Gray graph, ADAM graph, generalized Petersen graph
Published in RUP: 10.09.2025; Views: 1467; Downloads: 47
Full text (951,83 KB) |
4. Point-ellipse configurations and related topicsGábor Gévay, Nino Bašić, Jurij Kovič, Tomaž Pisanski, 2021, original scientific article Keywords: point-line configuration, conic section, point-ellipse configuration, point-conic configuration, Levi graph, Carnot's theorem
Published in RUP: 18.10.2021; Views: 5411; Downloads: 28
 Link to full text |
