20.500.12556/RUP-21614 On cubic vertex-transitive graphs of given girth A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs of vertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth almost nothing is known about the distinguishing costs of such graphs. We prove that cubic vertex-transitive graphs of girth 5 with two edge orbits have distinguishing cost 2, and prove the non-existence of infinite 3-arc-transitive cubic graphs of girth 6. distinguishing number distinguishing cost vertex-transitive cubic graphs automorphisms ločilno število ločilna teža točkovno-tranzitiven graf avtomorfizmi true false true Angleški jezik Slovenski jezik Članek v reviji 2025-08-27 10:01:10 2025-08-27 10:01:11 2025-09-05 03:02:17 0000-00-00 00:00:00 2025 0 0 str. 1-16 no. 1, [article no.] P1.12 Vol. 8 2025 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2025-08-19 519.17 2590-9770 10.26493/2590-9770.1724.18a 246737923 RAZ_Dobson_Edward_Tauscher_2025.pdf RAZ_Dobson_Edward_Tauscher_2025.pdf 1 7ADEA4A1B51F15426C5B429006A2187B 35936af87f52123b6520adafd981b76d5f05a3311a8873016830e96d8031f529 43d7f5f8-831c-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31415 https://adam-journal.eu/index.php/ADAM/article/view/1724 1 0ea9f9a8-831c-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31414 Fakulteta za matematiko, naravoslovje in informacijske tehnologije Inštitut Andrej Marušič 0 0 0