Project duration: 1 January 2025 – 31 December 2026

Project title: Advancements in graph theory: Exploring novel and established irregularity measures

Affiliation of the partner institution: Faculty of Natural Sciences and Mathematics, University of Montenegro, 81000 Podgorica

Project leader: Res. Assoc. Dr. Darko Dimitrov

Project type: Bilateral project

Brief description of the project:

In this project, we explore various recent developments in graph irregularities, focusing on the following directions:

Extremal problems: Irregularity measures play a crucial role in understanding graph structures, particularly in extremal problems that highlight extreme configurations. Building on our previous work, our goal is to characterise extremal trees with arbitrarily large maximal degrees using novel and established irregularity measures, such as the sigma irregularity, total sigma irregularity, and Collatz-Sinogowitz index.

Inverse irregularity problems: Addressing open inverse irregularity problems is another key objective of our project. These problems present significant challenges in graph theory, offering insights into graph structures and irregularity. By tackling these challenges, we aim to uncover new insights and contribute to advancements in the field.

Sensitivity and robustness of irregularity measures: Evaluating the sensitivity and robustness of irregularity measures is essential for accurately assessing their significance. Building upon our prior research, we aim to include newly introduced irregularity measures and to enhance and extend our understanding in this area.

The project is financed by: ARIS