### Customized Project N1-0208

Automorphisms and Isomorphisms of Finite Graphs

Project Title: Automorphisms and Isomorphisms of Finite Graphs

PI: Istvan Kovacs

Project Code: N1-0208.

Type of the Project: customized project.

Funding Organization: Slovenian Research Agency (ARRS).

Research Field (ARRS): 1.01.00 - Natural Sciences and Mathematics / Mathematics.

Duration: 1. 6. 2021 - 31. 5. 2024.

Project Category: B.

Yearly Range: 0.80 FTE (1.367 research hours).

Sicris profile of the project is here.

Research Organization:

University of Primorska, UP FAMNIT

Project Members:

- Dobson Edward Tauscher (ARRS code: 3410)
- Kovacs Istvan (ARRS code: 25997, PI)
- Miklavič Štefko (ARRS code: 21656)
- Morgan Luke (ARRS code: 52908)
- Orel Marko (ARRS code: 25610)
- Hujdurović Ademir (ARRS code: 32518)

Abstract:

Combinatorial structures with a high level of symmetry are often explored in applications to both natural and social sciences. In some of these applications there is a demand to compare two objects efectively. A mathematical model capturing this situation is a finite graph with non-trivial symmetries, and the underlying mathematical discipline is algebraic graph theory (AGT). The symmetry of a graph is measured by its automorphism group and the alikeness of objects is expressed by the concept of a graph isomorphism. In the core of ATIFG lies the Cayley isomorphism problem, a well-known and long-standing open problem in AGT. In the proposal we outline several (sub)-problems, which will serve as mile-stones in the final solution.