• PROJECT CODE: J1-70046
• PROJECT TITLE: Symmetries in Graphs via Simplicial Automorphisms
• PROJECT TEAM: Michael Mrissa, PhD; Balazs David, PhD; Miklos Kresz, PhD; Prof. Klavdija Kutnar, PhD
• PERIOD: 1. 3. 2026 – 28. 2. 2029
• BUDGET: 450,000,00 EUR
• FINANCING: Slovenian Research and Innovation Agency (ARIS)
• PROJECT COORDINATOR: University of Primorska, Andrej Marušič Institute (Slovenia)

Within the proposed project we ask for existence of semiregular automorphisms having the additional property that the corresponding quotient graphs preserve the valencies of the original graphs. More precisely, we require that the quotient “multigraphs” with respect to the orbits of a subgroup generated by a semiregular automorphism are in fact simple graphs. An automorphism satisfying this condition will be called simplicial. The aim of this proposal is to launch the project of determining which vertex-transitive graphs admit simplicial automorphisms by starting the analysis for the class of cubic vertex-transitive graphs. In particular, the proposed project aims to give a complete answer to the question which cubic vertex-transitive graph with a quasiprimitive automorphism group admit simplicial automorphisms of prime order. Existence of simplical automorphisms in other classes of graphs will also be considered. In addition, the concept of simplical automorphism will be applied to different open problems in algebraic graph theory.