Print Email Facebook Twitter Extremal graphs for threshold metric dimension Title Extremal graphs for threshold metric dimension Author Datema, Tobias (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Komjáthy, J. (mentor) Bishnoi, A. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics Project AM3000 Date 2022-07-14 Abstract In this thesis, we consider the threshold metric dimension problem of graphs, related to and motivated by source detection.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)), where dk is the distance function in a graph limited by the range k (the distance is denoted as being ∞ if the distance is larger than k). Our aim in this thesis is to construct such a graph that is extremal in size, that is: the vertex set V is as large as possible. We shall give such constructions with proof for optimality up to k = 3 and general mand a different construction with incomplete proof for optimality for general k and m. For any construction we will prove that each vertex is uniquely identified.Furthermore, we will compare our results to another paper with a similar conclusion about the extremal size of graphs with metric dimension m and a given diameter D. Subject graph theorymetric dimensionthreshold metric dimensionextremalthreshold To reference this document use: http://resolver.tudelft.nl/uuid:49f39b66-1c8a-4699-845d-cfe9f4138a41 Part of collection Student theses Document type bachelor thesis Rights © 2022 Tobias Datema Files PDF report_tdatema.pdf 1.25 MB Close viewer /islandora/object/uuid:49f39b66-1c8a-4699-845d-cfe9f4138a41/datastream/OBJ/view