Nina Šere (2020) *The independence number of a graph*. MSc thesis.

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## Abstract

In the master's thesis we are dealing with the independence number of a graph. We show, that the well-known problem 3-SAT is reducible to the corresponding decision problem, the so-called independent set problem, which proves that the independent set problem is NP-complete. We then determine the independence number for different graphs, including some very well known infinite families of graphs like complete graphs, multi-partite complete graphs, cycle graphs, hypercube graphs, etc. In the last part of the thesis we focus on the family of generalized Petersen graphs GP(n,k). Based on their construction it is clear, that n is the upper bound for the independence number for GP(n,k). Moreover, if n is odd, the upper bound is n-1. In the master's thesis we determine the exact value of the independence number for different values of parameter k.

Item Type: | Thesis (MSc thesis) | ||||||
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Keywords: | independent set, independence number, NP-completeness, generalized Petersen graphs | ||||||

Number of Pages: | 65 | ||||||

Language of Content: | Slovenian | ||||||

Mentor / Comentors: |
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Link to COBISS: | https://plus.si.cobiss.net/opac7/bib/peflj/27336195 | ||||||

Institution: | University of Ljubljana | ||||||

Department: | Faculty of Education | ||||||

Item ID: | 6371 | ||||||

Date Deposited: | 07 Sep 2020 09:38 | ||||||

Last Modified: | 07 Sep 2020 09:38 | ||||||

URI: | http://pefprints.pef.uni-lj.si/id/eprint/6371 |

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