20.500.12556/RUL-140304 Konsistentni cikli v ločno tranzitivnih grafih magistrsko delo Consistent cycles in arc-transitive graphs Za delovanje podgrupe grupe avtomorfizmov G na grafu Γ pravimo, da je cikel grafa G-konsistenten, če obstaja avtomorfizem, ki na njem deluje kot rotacija za eno vozlišče. V tem magistrskem delu se bomo ukvarjali s številom različnih orbit konsistentnih ciklov za končne in lokalno končne grafe. Za orbite konsistentnih ciklov si bomo ogledali njihovo prekrivanje in kratnost. Na grupi avtomorfizmov grafa bomo definirali metriko, s katero postane topološka grupa. Za zaprte podgrupe grupe avtomorfizmov bomo preverili, da je stabilizator vsakega vozlišča kompakten in zanje poiskali formulo za izračun števila orbit konsistentnih ciklov. Definirali bomo drevo prekrivanj grafa ter našli algoritem, ki ga izračuna. For a subgroup G of the automorphism group acting on a graph, we say that a cycle is G-consistent if there exists an element of G that acts on the cycle as a 1-step rotation. In this thesis, we will be studying the number of orbits of consistent cycles for finite and locally finite graphs. We will define their overlap and multiplicity. The group of automorphisms of a graph can be equipped with a metric, for which it is a topological group. For its closed subgroups, we can show that the stabilizer of every vertex is compact and find a formula to calculate the number of orbits of consistent cycles. We will also define the overlap tree of a graph and develop an algorithm to find it. konsistentni cikli drevo konsistentnih ciklov prekrivanje drevo prekrivanj lokalno končni grafi consistent cycles tree of consistent cycles overlap overlap tree locally finite graphs true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2022-09-14 08:15:04 2022-09-14 08:15:05 2024-05-29 12:12:13 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 127027 121345283 5355.pdf 5355.pdf 1 BE8DE400CC6427EE48E32931ECB57A98 d6d4aa8a67008630e776b4fbd43fe7cb257b39a5e3739542ab63c007032964ab 82967248-33f4-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=161012 Fakulteta za matematiko in fiziko 0 0 0