Recent work by Elder and Piggott has proven a new result in graph theory about locally-finite undirected simple geodetic graphs: if all isometrically embedded circuits of such a graph have length at most 5, then the diameter of any embedded circuit in it is at most 2.
This project aims to extend the result proven by Elder and Piggott to isometrically embedded circuits of length 7 or greater, while also searching for counterexamples where that does not hold true at such length, with the assistance of programming to explore and enumerate examples. If successful, this will lead to further insights into the theory of length-reducing rewriting systems, and also the construction of a general classification for all finite geodetic graphs.
University of Technology Sydney
John (Khang) is currently a second-year undergraduate student in the Bachelor of Computing Science at the University of Technology Sydney, majoring in Artificial Intelligence and Data Analytics.
After starting to delve into topics such as machine learning and data structures and algorithms, John has gained a deep appreciation for the mathematics that underpins all computer programs and models. In particular, courses covering probability, computation, graph theory and mathematical logic have been his favourites so far at university. John intends to explore some of those topics for his honours project in two years’ time. He believes the intersection of mathematics, statistics, and computer science will be the key to solving many current and future problems.
Outside of academic studies, John finds himself perpetually stuck in a dilemma of deciding how to spend his free time between working on personal programming projects, watching e-sports, and reading up on history. You can also occasionally find him walking around in a park with earphones on enjoying his favourite soundtracks.