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Molendijk, Thomas (author)The ktruncated metric dimension of a graph is the minimum number of sensors (a subset of the vertex set) needed to uniquely identify every vertex in the graph based on its distance to the sensors, where the sensors have a measuring range of k. We give an algorithm with the goal that given any tree and any value for the measuring range of the...bachelor thesis 2023
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Kloet, Pim (author)All organisms are built out of cellular tissue. Being able to recognise abnormalities in these tissues could be useful in recognizing cancerous cells. In this thesis we construct a mathematical model for cellular tissue based on its spatial structure. We consider cells as elements of the network. Touching cells are considered connected. Cells...bachelor thesis 2023
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Jonker, Stan (author)In this thesis, we examine the kernelbased spatial random graph (KSRG) model, which is a generalisation of many known models such as longrange percolation, scalefree percolation, the Poisson Boolean model and agebased spatial preferential attachment. We construct a KSRG from a vertex set V = Z^d, assigning each vertex v ∈ V a weight Wv...master thesis 2023
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van Velzen, Daan (author)Preferential Attachment models offer an explanation for why power laws are so common in realworld data. In these models, we start out with an initial network and add nodes one at a time. For each new node, we make m connections to existing nodes and if we define the attachment probability of attaching to a vertex to be proportional to its...master thesis 2022
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Datema, Tobias (author)In this thesis, we consider the threshold metric dimension problem of graphs, related to and motivated by source detection.<br/>We construct a graph G = (V,E) for a given set of sensors of size m: {s1, s2, ..., sm} and a range k > 0. We want that each node v ∈ V has a unique combination of distances (dk (s1, v),dk (s2, v), ...,dk (sm, v)),...bachelor thesis 2022
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Wassenaar, Vincent (author)A graph G=(V,E) is a mathematical model for a network with vertex set V and edge set E. A Random Graph model is a probabilistic graph. A Random Geometric Graph is a Random Graph were each vertex has a location in a space χ. We compare the ErdosRényi random graph, G(n,p), to the Random Geometric Graph model, RGG(n,r) where, in general we use r=c...bachelor thesis 2022
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Primavera, Alessandra (author)We consider the game cops and robbers, which is a pursuitevasion game played on a graph G. The cops and the robber take turns moving across the vertices of G, where the goal for the cops is to eventually catch the robber. Specifically, we study the cop number of G, i.e. the minimum number of cops that is needed to catch the robber on G. We...bachelor thesis 2022