1. Nut graphs with a prescribed number of vertex and edge orbitsNino Bašić, Ivan Damnjanović, 2026, original scientific article Abstract: A nut graph is a nontrivial graph whose adjacency matrix has a one-dimensional null space spanned by a vector without zero entries. Recently, it was shown that a nut graph has more edge orbits than vertex orbits. It was also shown that for any even $r \geq 2$ and any $k \geq r + 1$, there exist infinitely many nut graphs with r vertex orbits and k edge orbits. Here, we extend this result by finding all the pairs $(r, k)$ for which there exists a nut graph with $r$ vertex orbits and $k$ edge orbits. In particular, we show that for any $k \geq 2$, there are infinitely many Cayley nut graphs with $k$ edge orbits and $k$ arc orbits.
Keywords: nut graph, vertex orbit, edge orbit, arc orbit, Cayley graph, automorphism
Published in RUP: 09.01.2026; Views: 1120; Downloads: 8
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3. Operations on oriented mapsTomaž Pisanski, Gordon Ian Williams, Leah Berman, 2017, original scientific article Keywords: map, oriented map, truncation, medial, snub, flag graph, arc graph
Published in RUP: 16.03.2018; Views: 5292; Downloads: 175
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4. Nove karakterizacije v strukturni teoriji grafov : 1-popolno usmerljivi grafi, produktni grafi in cena povezanostiTatiana Romina Hartinger, 2017, doctoral dissertation Keywords: 1-perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, block-cactus graph, cobipartite graph, K4-minor-free graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product, price of connectivity, cycle transversal, path transversal
Published in RUP: 09.11.2017; Views: 7034; Downloads: 66
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8. On non-normal arc-transitive 4-valent dihedrantsIstván Kovács, Boštjan Kuzman, Aleksander Malnič, 2010, original scientific article Abstract: Let ▫$X$▫ be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group ▫$D_n$▫ such that ▫$X$▫ is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within ▫$D_n$▫. It is shown that ▫$X$▫ is isomorphic either to the lexicographic product ▫$C_n[2K_1]$▫ with ▫$n \geq 4$▫ even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.
Keywords: Cayley graph, arc transitivity, dihedral group
Published in RUP: 15.10.2013; Views: 6591; Downloads: 149
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