The isomorphism problem for directed acyclic graphs: an application to multivector fields

This thesis is based on a project developed by a group of researchers at the Faculty of Mathematics and Computer Science at the Jagiellonian University of Krakow. They study sampled dynamics using combinatorial multivector fields. Applying a decomposition into strongly connected components, it is possible to create a directed acyclic graph, called Morse graph, which is a description of the multivector field's global dynamics. Therefore the purpose of this thesis is to compare directed acyclic graphs. In the first chapter we describe the creation process of a Morse graph and an algorithm to study the graph isomorphism problem. The second chapter is dedicated to our personal work, so we describe four Python tests we developed to establish whether two directed acyclic graphs are definitely not isomorphic. In the third chapter we sum up many examples. The last chapter aims to present a possible way for the future work, that is to treat a combinatorial multivector filed as a finite topological space.