Comparing invariants of graph-theoretic ideals

In this project, we study a connection between graphs (also called networks) and algebraic objects known as ideals. Graph theory is a major branch of modern mathematics, with diverse applications to society and industry such as transportation system modelling and social media marketing. The simple yet fundamental algebraic structure of an ideal encodes important information about the structure of the corresponding graph. This encoding comes in the form of certain numbers, known as invariants, that are associated to the ideal. The regularity, projective dimension, and h-polynomial degree are three invariants that are widely studied in the literature. This project aims to investigate certain graph properties by computing and comparing these invariants. The regularity, in particular, is closely related to the existence of cycles in the corresponding graph, which is of great interest in both pure and applied graph theory. This project will leverage supercomputer resources to compute these invariants and develop new results for several classes of graphs and ideals. Such computations will prove invaluable to other researchers in this area as they formulate questions for further study.

Faculty Supervisor:

Adam Van Tuyl

Student:

Partner:

Osaka University

Discipline:

Mathematics

Sector:

Education

University:

McMaster University

Program: