Research Interests

• Graph Theory and Applications (Metric Graph Theory, Spectral Graph theory, Chemical Graph Theory)
• Complex Networks
• Cluster Analysis

Degrees

• PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia, 2011.
• BS in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2005.

Publications

1. S. Majstorović Ergotić, On Unicyclic Graphs with Minimum Graovac-Ghorbani Index, Mathematics (2024), prihvaćen za objavljivanje
   Abstract

   In discrete mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Chemical graph theory is concerned with non-trivial applications of graph theory to the solution of molecular problems. Its main goal is to use numerical invariants to reduce the topological structure of a molecule to a single number that characterizes its properties. Topological indices are numerical invariants associated with the chemical constitution for the purpose of correlation of chemical structures with various physical properties, chemical reactivity or biological activity. They have found important application in predicting the behavior of chemical substances. The Graovac-Ghorbani index is a topological descriptor that has predictive potential compared to analogous descriptors. It is used to model both the boiling point and melting point of molecules and is applied in the pharmaceutical industry. In the last years, the number of publications on its mathematical properties has increased. The aim of this work is to partially solve an open problem, namely to find the structure of unicyclic graphs that minimize the Graovac-Ghorbani index. We characterize unicyclic graphs with even girth that minimize the Graovac-Ghorbani index, while we present partial results for odd girth. As an auxiliary result, we compare the Graovac-Ghorbani indices of paths and cycles with an odd number of vertices.
2. R. Scitovski, K. Sabo, P. Nikić, S. Majstorović Ergotić, A new efficient method for solving the multiple ellipse detection problem, Expert systems with applications 222/119853 (2023)
   Abstract

   In this paper, we consider the multiple ellipse detection problem based on data points coming from a number of ellipses in the plane not known in advance. In so doing, data points are usually contaminated with some noisy errors. In this paper, the multiple ellipse detection problem is solved as a center-based problem from cluster analysis. Therefore, an ellipse is considered a Mahalanobis circle. In this way, we easily determine a distance from a point to the ellipse and also an ellipse as the cluster center. In the case when the number of ellipses is known in advance, an optimal partition is searched for on the basis of the -means algorithm that is modified for this case. Hence, a good initial approximation for M-circle-centers is searched for as unit circles with the application of a few iterations of the well-known DIRECT algorithm for global optimization. In the case when the number of ellipses is not known in advance, optimal partitions with clusters for the case when cluster-centers are ellipses are determined by using an incremental algorithm. Among them, the partition with the most appropriate number of clusters is selected. For that purpose, a new Geometrical Objects-index (GO-index) is defined. Numerous test-examples point to high efficiency of the proposed method. Many algorithms can be found in the literature that recognize ellipses with clear edges well, but that do not recognize ellipses with unclear or noisy edges. On the other hand, our algorithm is specifically used for recognition of ellipses with unclear or noisy edges.
3. S. Majstorović Ergotić, Maximizing Graovac-Ghorbani Index of Trees with Fixed Maximum Degree, MATCH Communications in Mathematical and in Computer Chemistry 90/3 (2023), 673-684
4. R. Scitovski, S. Majstorović Ergotić, K. Sabo, A combination of RANSAC and DBSCAN methods for solving the multiple geometrical object detection problem, Journal of Global Optimization 79/3 (2021), 669-686
   Abstract

   In this paper we consider the multiple geometrical object detection problem. On the basis of the set $A$ of data points coming from and scattered among a number of geometrical objects not known in advance, we should reconstruct or detect thosegeometrical objects. A new very efficient method for solving this problem based on avery popular RANSAC method using parameters from DBSCAN method is proposed.Thereby, instead of using classical indexes for recognizing the most appropriatepartition, we use parameters from DBSCAN method which define the necessaryconditions proven to be far more efficient.Especially, the method is applied to solving multiple circle detection problem. In this case, we give both the conditions for the existence of the best circle as arepresentative of the data set and the explicit formulas for the parameters of the bestcircle. In the illustrative example we consider the multiple circle detection problem for the datapoint set $A$ coming from $5$ intersected circles not known in advance. Using Wolfram Mathematica, the proposed method needed between 0.5 - 1 sec to solve this problem.
5. M. Knor, S. Majstorović Ergotić, A. Teo Masha Toshi, R. Škrekovski, I. Yero, Graphs with the edge metric dimension smaller than the metric dimension, Applied mathematics and computation 401 (2021)
6. M. Knor, S. Majstorović Ergotić, R. Škrekovski, Graphs preserving total distance upon vertex removal, Electronic Notes in Discrete Mathematics 68 (2018), 107-112
7. M. Knor, S. Majstorović Ergotić, R. Škrekovski, Graphs preserving Wiener index upon vertex removal, Applied mathematics and computation 338 (2018), 25-32
8. M. Knor, S. Majstorović Ergotić, R. Škrekovski, Graphs whose Wiener index does not change when a specific vertex is removed, Discrete Applied Mathematics 238 (2018), 126-132
9. S. Majstorović Ergotić, K. Sabo, J. Jung, M. Klarić, Spectral methods for growth curve clustering, Central European Journal of Operations Research 26/3 (2018), 715-737
   Abstract

   The growth curve clustering problem is analyzed and its connec- tion with the spectral relaxation method is described. For a given set of growth curves and similarity function, a similarity matrix is defined, from which the corresponding similarity graph is constructed. It is shown that a nearly op- timal growth curve partition can be obtained from the eigendecomposition of a specific matrix associated with a similarity graph. The results are illus- trated and analyzed on the set of synthetically generated growth curves. One real-world problem is also given.
10. S. Majstorović Ergotić, A. Klobučar, T. Došlić, Domination Numbers of m-cactus chains, Ars Combinatoria 125 (2016), 11-22
11. S. Majstorović Ergotić, G. Caporossi, Bounds and relations involving the adjusted centrality of a tree, Graphs and Combinatorics 31/6 (2015), 2319-2334
12. S. Majstorović Ergotić, D. Stevanović, A note on graphs with the largest eigenvalue of modularity matrix equal to zero, Electronic Journal of Linear Algebra 27 (2014), 611-618
13. S. Majstorović Ergotić, T. Došlić, A. Klobučar, K-domination on hexagonal cactus chains, Kragujevac Journal of Mathematics 36/2 (2012), 335-347
14. S. Majstorović Ergotić, K-domination sets on double linear hexaghonal chains, Aplimat - Journal of applied mathematics 3/3 (2010), 77-86
15. S. Majstorović Ergotić, A. Klobučar, I. Gutman, Tricyclic Biregular Graphs Whose Energy Exceeds the Number of Vertices, Mathematical Communications 15/1 (2010), 213-222
16. I. Gutman, A. Klobučar, S. Majstorović Ergotić, C. Adiga, Biregular Graphs Whose Energy Exceeds the Number of Vertices, MATCH Communications in Mathematical and in Computer Chemistry 62/3 (2009), 499-508
17. S. Majstorović Ergotić, A. Klobučar, I. Gutman, Triregular Graphs Whose Energy Exceeds the Number of Vertices, MATCH Communications in Mathematical and in Computer Chemistry 62/3 (2009), 509-524

1. S. Majstorović Ergotić, A. Kolos Csaba, A. Vaskovi, Spectral Clustering of Survival Curves, International Symposium of Operational Research SOR'19, Bled, Slovenia, 2019, 81-87

1. S. Majstorović Ergotić, M. Rechner, Turanov teorem, Math.e : hrvatski matematički elektronski časopis 42 (2023), 28-42
2. S. Majstorović Ergotić, D. Begović, Niz stupnjeva grafa, Osječki matematički list 20/1 (2020), 39-52
3. S. Majstorović Ergotić, K. Vincetić, Totalna zbrka, Osječki matematički list 17/2 (2017), 109-123
4. K. Vincetić, S. Majstorović Ergotić, Zanimljivi zadatci s brojem 2017, Poučak 72/18 (2017), 6-23
5. S. Majstorović Ergotić, L. Boras, Petersenov graf, Math.e : hrvatski matematički elektronski časopis 27 (2015)
6. S. Majstorović Ergotić, Dirichletov princip, Osječki matematički list 6 (2006), 99-105

Projects

• “Regionalni znanstveni centar Panonske Hrvatske”, stručni projekt, nositelj: Osječko-baranjska županija, 2022.-2024.

• “Modeling adsorption of nanostructures: A graph-teoretical approach, bilateral project, 2016.-2017.

Project leader (on Croatian side): Tomislav Došlić, Faculty of Civil Engineering, University of Zagreb

Project leader (on Slovenian side): Riste Škrekovski, Faculty of Mathematics and Physics, University of Ljubljana

• “Neke primjene geometrijskih reprezentacija u grafovima“ u sklopu kolaborativnog projekta „Geometrijske reprezentacije i simetrije grafova i druge diskretne strukture i primjene u znanosti pod vodstvom prof. dr. sc. A. Klobučar,  2011.-2014.

• “Pasivna kontrola mehaničkih modela“ pod vodstvom prof.dr.sc.N.Truhara, 2009.-2014.

Professional Activities

Editorial Board

• Topical Advisory Panel in  Mathematics (MDPI) (since 2021)

•   HMD – Croatian Mathematical Society, Department Osijek
•   HDOI – Croatian Operational Research Society
•   EMS – European Mathematical Society

Study Visits Abroad and Professional Improvements

• DAAD Biomedical Image Analysis and Bioinformatics – Intensive course, Vrnjačka Banja, Serbia, September 2020
• GERAD – Group for Research in Decision Analysis, Montreal, Canada, October, 2011.
• Summer School of the Marie Curie ITN ‘Environmental ChemoInformatics’, Verona, Italy, June 2012
• DAAD- Graph Spectra and Applications- Intensive course, Vrnjačka Banja, Serbia, September 2012
• DAAD- Linear Optimal Control of Dynamic Systems, Osijek, Croatia, September 2013
• Summer School in Discrete Mathematics, Rogla, Slovenia, June 2015
• Montanuniversitat Loeben, Loeben, Austria, September 2015  (ERASMUS+ 2014/2015)
• Montanuniversitat Loeben, Loeben, Austria, September 2015  (ERASMUS+ 2015/2016)
• DAAD – Approximation theory and Applications, Sozopol, Bulgaria, June 2016
• DAAD – Krylov Subspaces and Applications, Golem, Kavaja, Albania, September 2016
• Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, 1.03.-5.03. 2017
• Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, 16.12.-21.12. 2017
• Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, August 2018 (ERASMUS+ 2017/2018)
• Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, June 2021 (ERASMUS+ 2021/2022)
• Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, October 2022 (ERASMUS+ 2022/2023)

• “Types of domination on m-ary chain cacti”, GERAD-Group for Research in Decision Analysis, Montreal, Canada, October 2011
• “Indivisible graphs”, Technische universitat, Graz, Austria, January 2015
• “Spectral methods for growth curve clustering”, Corvinus University, Budapest, Hungary, April 2018

Service Activities

• Zimska matematička škola (Winter math school) 2005.-2006. “Tetivno-tangencijalni četverokuti”
• Pripreme za natjecanje IMC,  2015.
• Koordinatorica priprema za međunarodna studentska natjecanja iz matematike: Vojtech 2016, IMC 2017, IMC 2018
• Član organizacijskog odbora međunarodne konferencije CroCoDays 2016 , CroCoDays 2018, CroCoDays 2020, CroCoDays 2022
• Član programskog odbora međunarodne konferencije  MSGT 2023
• IAESTE – mentor   od ak.god. 2016/2017 – ….
• Koordinatorica za Festival znanosti od 2018. -…
• Festival znanosti 2018: “Fourierova otkrića”
• Festival znanosti 2019: “Neriješeni problem bojenja ravnine”
• Festival znanosti 2022: “Eulerova otkrića”
• Član organizacijskog odbora međunarodne studentske konferencije GREEN 2018
• Član organizacijskog odbora međunarodne studentske konferencije GREEN 2022
• Član organizacijskog odbora međunarodne konferencije VODA ZA SVE 2019
• Večer matematike 2018: “Modeliranje pomoću grafova”
• Član organizacijskog odbora STEM games 2021

Teaching

Konzultacije (Office Hours):

• Konzultacije su moguće po dogovoru.

Teme za diplomske radove (Master thesis topics):

• Teme se dogovaraju izravno na konzultacijama s nastavnikom.

Present and past courses

I am currently teaching

1. Graphs and applications
2. Complex networks
3. Combinatorial and Discrete Mathematics
4. Mathematics III (Faculty of Civil Engineering and Architecture, Osijek)

Personal

• Birthdate: April 13
• Birthplace: Osijek, Croatia
• Citizenship: Croatian