Bratislava, Slovakia


Room: M144

Department: Katedra algebry a geometrie

University: Fakulta matematiky, fyziky a informatiky Univerzity Komenskeho
Mlynska dolina, 842 48, Bratislava

Phone: +421 (0)2 602 95642 (office)


Office of Doctoral Studies: F2-92, +421 (0)2 602 95194




8:10 - 9:40, C, 1-MMN-120/22 and 1-AIN-152/22, Linear Algebra
11:00 - 11:30, F2 - 92, Uradne hodiny na referate DRS / Office hours doctoral studies


11:00 - 11:30, F2 - 92, Uradne hodiny na referate DRS / Office hours doctoral studies



8:10 - 9:40, M-105, 2-MAT-224/09, Linear Coding
09:50 - 11:20, M213, Graph Theory Seminar
13:30 - 14:00, F2- 92, Uradne hodiny na referate DRS / Office hours doctoral studies
14:10 - 15:50, M-144, FMFI.KAG/2-MAT-231/09, Data Encryption


13:00 - 14:30, M-V, Algebraic Graph Theory Seminar


Ph.D. Mathematics/Computer Science (minor), May, 1995

University of Nebraska-Lincoln, Lincoln, Nebraska

Research specialty: Algebraic Combinatorics

Dissertation: Vertex-transitive graphs and maps and their automorphism groups

Advisor: Professor Spyros S. Magliveras

RNDr., summa cum laude, Mathematics
Comenius University, Bratislava, Slovakia, 1988



L. Eze and R. Jajcay, Recursive constructions of graphs of large girth and given degree,
ITAT 2022 Proceedings, CEUR Workshop Proceedings Vol. 3226 (2022) 204 - 213.

G. Araujo-Pardo, A. Ramos Rivera, R. Jajcay, and T. Szonyi, On a relation between bipartite biregular cages, block designs
and generalized polygons, Journal of Combinatorial Designs 30 (7) (2022) 479-496.

R. Jajcay, P. Potocnik and S. Wilson, On the Cayleyness of Praeger-Xu graphs,
J. of Comb. Theory, Ser. B 152 (2022) 55-79.

S. Filipovski and R. Jajcay, A connection between a question of Bermond and Bollobas and Ramanujan graphs,
Acta Applicandae Mathematicae 175 (1), 1 (2021).

A. Zavrtanik Drglin, S. Filipovski, R. Jajcay and T. Raiman, Extremal edge-girth-regular graphs,
Graphs and Combinatorics 37 (6) 2139-2154 (2021).

S. Filipovski and R. Jajcay, Bounds for the energy of graphs,
Mathematics 9 (2021), 1687.

R. Jajcay and T. Raiman, Spectra of orders for k-regular graphs of girth g,
Discussiones Mathematicae Graph Theory 41 (2021) 1115-1125.

R. Jajcay and M. Lekar, The impact of emigration on Slovak mathematics - the case of the Bratislava Graph Theory Seminar,
Math. Intell. 43, No. 1, 45-53 (2021).

R. Jajcay, T. Jajcayova, N. Szakacs and M.B. Szendrei, Inverse monoids of partial graph automorphisms,
Journal of Algebraic Combinatorics 53 (3), 829-849 (2021).


Member of the Editorial Board of Ars Mathematica Contemporanea
and Acta Mathematica Universitatis Comenianae


Educational Excellence Award, College of Arts and Sciences, ISU, April 1999

Teaching Award awarded by the Dean of FMFI UK, Faculty of Mathematics, Physics and Informatics of the Comenius University, November, 2018


Christian Rubio Montiel, January 1 - December 31, 2016, currently at FES Acatlan, National Autonomous University of Mexico

Sara Sabrina Zemljic, December 1, 2017 - November 30, 2018

Slobodan Filipovski, December 1, 2019 - November 30, 2020


Milan Lekar, PhD., 2022, Comenius University, The impact of emigration on the development of Mathematics in Slovakia

Slobodan Filipovski, PhD., 2018, University of Primorska, On extremal graphs of given degree and diameter/girth


Branislav Boran, MSc, 2022, Comenius University, Vlastnosti a symetrie linearnych kodov generovanych incidencnymi maticami regularnych grafov s malym obvodom

Marek Murin, MSc, 2021, Comenius University, Two-dimensional recurrence relations and enumeration of locally testable matrices

Dominik Holly, MSc, 2020, Comenius University, Codes with Prescribed Automorphism Groups

Ajda Zavrtanik Drglin, MSc, 2019, University of Ljubljana, Girth-Regular and Edge-Girth-Regular Graphs

Nicole Durisova, MSc, 2019, Comenius University, Rekurentne postupnosti v linearnej algebre

Juraj Karlubik, MSc, 2018, Comenius University, Vyuzitie softveroveho balika GAP na vytvaranie a testovanie hypotez v algebraickej teorii grafov

Katarina Jasencakova, MSc, 2017, Comenius University, m-Spanning Generalized Petersen Graphs

Viktor Hirschner, MSc, 2017, Comenius University, Recursive Constructions of Regular Graphs

Martin Bachraty, MSc, 2015, Comenius University, Powers of Skew-Morphisms

Tomas Peitl, MSc, 2015, Comenius University, Applications of Number Theory to Homomorphic Encryption

Michael Cameron , MSc, 1998, Indiana State University, Constructing Regular Cayley Maps Using Computers


Juraj Belohorec, 2022, Mathematical and Algorithmic Foundations of Attacks on the Knapsack Problem Based Cryptographic Protocols

Alexandra Racikova, 2022, Matematicke zaklady zdielania tajomstva v kryptografii

Damian Konig, 2020, Vyuzitie metod linearnej algebry v autentifikacii s nulovou stratou informacie

Jakub Skoda, 2020, Discrete Logarithm and Integer Factorization

Jana Valigurska, 2019, Symmetric Codes

Veronika Zajceva, 2017, Vyuzitie metod linearnej algebry na vyhladavanie extremalnych grafov

Justina Karlovska, 2017, Vyuzitie metod linearnej algebry na vyhladavanie extremalnych grafov

Veronika Martisova, 2016, Aplikacie teorie sifrovania v internetovej komunikacii

Kamil Bena, 2016, Perfektne linearne a nelinearne kody

Katarina Dunikova, 2015, Applications of Game Theory in Pricing Strategy Selection

Katarina Jasencakova, 2015, Use of Lifting Techniques in Vertex-Transitive Graph Constructions

Martin Bachraty, 2013, Powers of Skew-Morphisms


Vyuzitie algebraickych a vypoctovych metod na riesenie klasickych problemov extremalnej teorie kombinatorickych struktur,
VEGA 1/0596/17, 2017-2019 (with M. Macaj)

Algebraicke, topologicke a kombinatoricke metody v studiu diskretnych struktur,
APVV-15-0220, 2016-2018 (with M. Skoviera)

Graphs and Related Structures,
VEGA 1/0474/15, 2015-2017 (with M. Skoviera)

Applications of inverse semigroups in combinatorics,
VEGA 1/0577/14, (with T.B. Jajcayova)

Project: Mobility,
ITMS code: 26110230082, (with R. Nedela)

National Science Foundation of China,
NSFC 11371307, (with Yan Wang)

Algebraic, Topological and Combinatorial Structures on Graphs,
APVV, 2011 - 2014, (with M. Skoviera)

Research and Development Cooperation Slovakia -- China,
2011 - 2012, (with R. Nedela)

Algebraic, Combinatorial and Topological Structures on Graphs,
APVV, 2008 - 2010 (with M. Skoviera)

Symmetric graphs and maps,
VEGA, 2002 - 2004 (with J. Siran)

US - Slovenia cooperation,
awarded by the Slovenian Ministry of Science, 2002 - 2006 (with D. Marusic)

National Research Council's Collaboration in Basic Science and Engineering (COBASE),
2002 (with D. Marusic)

Summer research grants
awarded by the Indiana State University Research Council, 1996, 1998, 2004, 2009


August 26 - 30, 2019, Bratislava, Slovakia

Trojkralova konferencia 2016
January 4, 2016, Bratislava, Slovakia

IWONT 2014, The 6th International Workshop on Optimal Network Topologies
June 30 - July 4, 2014, Bratislava, Slovakia

Midwest Graph Theory Conference, MIGHTY LII
Terre Haute, IN, April 27-28, 2012

Indiana Section of the Mathematical Association of America
Terre Haute, IN, April 2-3, 2004

Midwestern Conference on Combinatorics, Cryptography and Computing
Terre Haute, IN, Oct.30 - Nov. 1, 1997