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Konsistentni cikli v ločno tranzitivnih grafih : magistrsko delo
ID Lekše, Maruša (Author), ID Potočnik, Primož (Mentor) More about this mentor... This link opens in a new window

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Abstract
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.

Language:Slovenian
Keywords:konsistentni cikli, drevo konsistentnih ciklov, prekrivanje, drevo prekrivanj, lokalno končni grafi
Work type:Master's thesis/paper
Organization:FMF - Faculty of Mathematics and Physics
Year:2022
PID:20.500.12556/RUL-140304 This link opens in a new window
COBISS.SI-ID:121345283 This link opens in a new window
Publication date in RUL:14.09.2022
Views:773
Downloads:88
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Secondary language

Language:English
Title:Consistent cycles in arc-transitive graphs
Abstract:
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.

Keywords:consistent cycles, tree of consistent cycles, overlap, overlap tree, locally finite graphs

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