Research:

Primary interest: preserver problems, graph cores, etc. 

Current research involves Matrix Theory with an addition of the theory of Finite Fields,  Algebraic Graph Theory (mainly Spectral and Chromatic Graph Theory), some Geometry, and some Mathematical Physics.

Journal publications/manuscripts 

• • M. Orel, D. Višnjić, The distance function on Coxeter-like graphs and self-dual codes. Finite Fields Appl. 103 (2025), paper 102580, 51 pp. (open access) https://doi.org/10.1016/j.ffa.2025.102580 

  • M. Orel, A family of non-Cayley cores based on vertex-transitive or strongly regular self-complementary graphs. Preprint available at arXiv.

Based on the suggestions by a referee/editor at the initial submission, and a boost from the administrative rules at the home university, the manuscript eventually split into the following five parts. In the splitting process, some of the results generalized substantially and some results were added  (see 4. and 5. in particular):

1.  M. Orel,  The automorphism group of a complementary prism. J. Combin. Theory Ser. B. 169 (2024), 406-429. (open access)  https://doi.org/10.1016/j.jctb.2024.07.004

2. M. Orel, The core of a complementary prism.  J. Algebraic Combin. 58 (2023), 589-609.  (open access)  https://doi.org/10.1007/s10801-023-01236-4

3. M. Orel, The core of a vertex-transitive complementary prism. Ars Math. Contemp. 23(4)  (2023), paper #P4.07.  (open access) https://doi.org/10.26493/1855-3974.3072.3ec

4. M. Orel, The core of a vertex-transitive complementary prism of a lexicographic product. Art Discrete Appl. Math.  6 (2023), paper #P3.10. (open access) https://doi.org/10.26493/2590-9770.1623.7f0

5. M. Orel, The Cheeger number and Hamiltonian properties of complementary prisms. Submitted.  

             Slides of some (early) talk presentations at the conferences:  

                a) 8th European Congress of Mathematics  

                b) Combinatorial Designs and Codes

• • A. Hujdurović, K. Kutnar, B. Kuzma, D. Marušič, Š. Miklavič, M. Orel, On intersection density of transitive groups of degree a product of two odd primes. Finite Fields Appl. 78 (2022), 101975. https://doi.org/10.1016/j.ffa.2021.101975 Preprint available at arXiv.  

  • M. Orel, Nonstandard rank-one nonincreasing maps on symmetric matrices. Linear and Multilinear Algebra 67(2) (2019), 391-432. Available here.  DOI: 10.1080/03081087.2017.1419456

  • M. Orel, On Minkowski space and finite geometry. J. Combin. Theory Ser. A. 148 (2017), 145-182. http://dx.doi.org/10.1016/j.jcta.2016.12.004 

  • M. Orel, On generalizations of  the Petersen and the Coxeter graph. Electron. J. Combin. 22(4) (2015), Paper #P.4.27. Available freely online.

  • M. Orel, Adjacency preservers on invertible hermitian matrices I. Linear Algebra Appl. 499 (2016), 99-128. http://dx.doi.org/10.1016/j.laa.2014.10.034  

  • M. Orel, Adjacency preservers on invertible hermitian matrices II. Linear Algebra Appl. 499 (2016), 129-146. http://dx.doi.org/10.1016/j.laa.2014.10.033  

  • M. Orel, Adjacency preservers, symmetric matrices, and cores, J. Algebraic Combin. 35 (4) (2012), 633-647. http://dx.doi.org/10.1007/s10801-011-0318-0

  • G. Dolinar, A. E. Guterman, B. Kuzma, M. Orel, On the Polya permanent problem over finite fields, European J. Combin. 32 (1) (2011), 116-132. http://dx.doi.org/10.1016/j.ejc.2010.07.001

  • M. Orel, B. Kuzma, Additive rank-one nonincreasing maps on hermitian matrices over the field GF(22), Electron. J. Linear Algebra 18 (2009), 482-499. Available freely online.

  • M. Orel, A note on adjacency preservers on hermitian matrices over finite fields, Finite Fields Appl. 15(4) (2009), 441-449. http://dx.doi.org/10.1016/j.ffa.2009.02.005

  • M. Orel, Nonbijective idempotents preservers over semirings,  J. Korean Math. Soc. 47 (4) (2010), 805-818. Available freely online.

  • M. Orel, B. Kuzma, Additive maps on Hermitian matrices, Linear Multilinear Algebra 55 (6) (2007), 599-617. http://dx.doi.org/10.1080/03081080701265140

  • B. Kuzma, M. Orel, Additive mappings on symmetric matrices, Linear Algebra Appl. 418 (1) (2006), 277-291. http://dx.doi.org/10.1016/j.laa.2006.02.010

Chapters in books

• • M. Orel, Preserver problems over finite fields, in: J. Simmons (Ed.), Finite Fields: Theory, Fundamental Properties and Applications, Nova Science Publishers, New York, 2017, pp. 1-54.          

(This chapter describes a connection between the study of preserver problems in matrix theory and the study of graph homomorphisms and cores in graph theory. It is written for mathematicians working in either of these two research areas. Graph theorists may find new motivation and applications for their research, while matrix theorists may find new techniques to solve preserver problems. Finally, the chapter surveys also some connections with finite geometry, where an increasing number of examples show that certain problems in finite geometry are related to the study of preserver problems and the study of graph homomorphisms.)  

Proceedings

• • G. Dolinar, A. Guterman, B. Kuzma, and M. Orel. Permanent versus determinant over a finite field.  Sovrem. Mat. Prilozh. Vol. 80, Proceedings of the International Conference ``Modern Algebra and Its Applications'' (Batumi, 2011), Part 1, 2012. English translation:  J. Math. Sci. (N. Y.) 193 (3) (2013), 404-413. http://dx.doi.org/10.1007/s10958-013-1469-4

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