Buitenhuis, Egbert Jan (2023) Invariants of Planar Random Geometric Graphs. Bachelor's Thesis, Mathematics.
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Abstract
In this paper we look at Random Geometric Graphs, these are graphs constructed from random distributed points on a space and with vertices connected by an edge if they are sufficiently close to each other. We are specifically interested in the case where the vertices are distributed on the plane. We also give attention to the special case where the distribution is the uniform distribution on the unit-square. Furthermore, the threshold distance for connecting pairs of vertices is chosen such that it fixes the expected average degree of each vertex. In these Random Geometric Graphs, we are interested in several graph invariants. Our main focus lies on the clique number ω, the maximum number points that are all pair-wise connected, and the chromatic number χ, the minimum number of colours needed to colour the vertices such that no two adjacent vertices are of the same colour. A large part of this paper is inspired by the paper of McDiarmid [Colin McDiarmid. “Random channel assignment in the plane”. In: Random Structures and Algorithms 22.2 (Mar. 2003)].
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Bonnet, G.F.Y. and Muller, T. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 16 Nov 2023 13:18 |
| Last Modified: | 16 Nov 2023 13:18 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/31646 |
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