Povezanost grafov

NUNČIČ, ALJAŽ (author), Robič, Borut (mentor)

Povezanost grafa nam pove, koliko povezav oziroma vozlišč moramo odstraniti, da graf postane nepovezan. Tako poznamo povezavno povezanost in vozliščno povezanost grafa. Na začetku bom predstavil nekaj izrekov, ki se nanašajo na povezanost grafov. Nato bom opisal algoritme za preverjanje povezanosti grafov, ki služijo tudi kot orodje za preverjanje uspešnega razbitja grafov. V zadnjem delu pa bom najprej predstavil reševanje problema minimalnega prereza z algoritmom za največji pretok, nato pa še druge naprednejše in bolj prilagojene algoritme za ta problem. V zaključku bom povzel vse ključne ugotovitve. Diplomska naloga tako predstavlja osnovni pregled problema povezanosti grafov.

• Language: Slovenian
• Keywords: graf, povezanost, povezavna povezanost, vozliščna povezanost
• Work type: Bachelor thesis/paper
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2019
• PID: 20.500.12556/RUL-109867
• COBISS.SI-ID: 1538319299
• Publication date in RUL: 09.09.2019

NUNČIČ, ALJAŽ, 2019, Povezanost grafov [online]. Bachelor’s thesis. [Accessed 8 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=109867

Secondary language

• Language: English
• Title: Graph Connectivity

Abstract

Graphs connectivity tells us how many edges or vertices must be removed from a graph so that the graph becomes disconnected. This induces the notations of the edge and vertex connectivity of a graph. In this thesis, I will first present some of the theorems related to graph connectivity. Then I will describe algorithms for checking whether or not a graph is connected, which can also be used to check whether or not a graph has been successfully split. Next, I will show how the min-cut problem is solved using the algorithm for maximum flow. Then, I will continue with presentation of some advanced and more adapted algorithms for the considered problem. Finally, I will conclude the thesis with a summary of the key findings. The thesis is thus a basic overview of the problem of graph connectivity.

• Keywords: graph, connectivity, edge connectivity, vertex connectivity