Simetrije grafovskih produktov / Symmetries of Graph Products

Projekt “Simetrije produktov grafov” se osredotoča na matematično analizo simetrij pri Kartezičnih in direktnih produktih grafov.

Cilj je rešiti odprta vprašanja, povezana z avtomorfizmi teh produktov in njihovim odnosom do lastnosti osnovnih grafov.

Vodja projekta je Ademir Hujdurović, sodelujejo pa raziskovalci iz Slovenije in tujine.

Projekt naslavlja ključna vprašanja, kot so pogoji za Cayleyjeve lastnosti Kartezičnih produktov in analiza stabilnosti grafov.

Metodologija vključuje algebrske in kombinatorične pristope ter uporabo Schurjevih kolobarjev.

Cilji vključujejo razumevanje stabilnosti Cayleyevih grafov, asimptotičnih lastnosti stabilnih grafov in pogojev za nestabilnost krepko regularnihgrafov.

Rezultati bodo prispevali k teoretičnemu razvoju na področju teorije grafov in imeli potencialne aplikacije v industriji, na primer pri optimizacijiomrežij.

Projekt bo izveden na Univerzi na Primorskem.

Predvidene so tudi aktivnosti za širjenje znanja, kot so delavnice, seminarji in poletne šole.

The project “Symmetries of Graph Products” focuses on the mathematical analysis of symmetries in Cartesian and direct graph products.

Its goal is to solve open problems related to the automorphisms of these products and their connections to the properties of the base graphs.

Led by Ademir Hujdurović, the project involves researchers from Slovenia and abroad.

The project addresses key questions, such as the conditions for the Cayley properties of Cartesian products and the analysis of graph stability.

The methodology combines algebraic and combinatorial approaches with the use of Schur rings.

Objectives include understanding the stability of Cayley graphs, asymptotic properties of stable graphs, and conditions for the instability of stronglyregular graphs.

The results will contribute to theoretical advancements in graph theory and have potential applications in industry, such as network optimization.

The project will be conducted at the University of Primorska.

Outreach activities, including workshops, seminars, and summer schools, are also planned.