Small-world and ultrasmall-world phenomena in kernel-based spatial random graphs

In this thesis, we examine the kernel-based spatial random graph (KSRG) model, which is a generalisation of many known models such as long-range percolation, scale-free percolation, the Poisson Boolean model and age-based spatial preferential attachment. We construct a KSRG from a vertex set V = Z^d, assigning each vertex v ∈ V a weight Wv...

Extremal graphs for threshold metric dimension

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 &gt; 0. We want that each node v ∈ V has a unique combination of distances (dk (s1, v),dk (s2, v), ...,dk (sm, v)),...

Modelling bivariate exposure distributions for Out of Home advertising

Out of Home advertising is traditional outdoor advertising. Over the last decade the digital Out of Home advertising possibilities have grown substantially. These possibilities include hour-based advertisement schedules, rapidly implemented changes to advertisements and obtaining location data from consumers being exposed to advertisements....

The Game of Cycles

The Game of Cycles, invented by Francis Su (2020, p.51) is an impartial game played on a graph, where players take turns marking an edge according to a set of rules. Together with the game, there also came a conjecture that gives a condition for whether a specific position is winning or losing. Proving or disproving this conjecture is the main...