PUBLICATIONS AND PROFESSIONAL ACTIVITIES


R. Jajcay, J. Jooken, and I. Porupsanszki, On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration,
submitted for publication.

T.B. Jajcayova, R. Jajcay, Gy. Kiss, and I. Porupsanszki, Extremal Totally Regular Mixed Graphs and Partially Oriented Incidence Graphs
of Projective and Biaffine Planes, submitted for publication.

L. Eze and R. Jajcay, Analogues of Bermond-Bollobas Conjecture for Cages Yield Expander Families,
submitted for publication.

K. Hu and R. Jajcay, Cyclic complementary extensions and skew-morphisms,
submitted for publication.

T.B. Jajcayova and R. Jajcay, Totally Regular Mixed Graphs Constructed from the CD(n,q) Graphs of Lazebnik, Ustimenko and Woldar,
accepted for publication in ADAM.

T.B. Jajcayova and R. Jajcay, Generalizations of Cayley graphs to uniform hypergraphs,
Art Discrete Appl. Math., 2024, doi:10.26493/2590-9770.1606.28a

S. Gyurki, R. Jajcay, P. Janos, J. Siran and Y. Wang, Using bi-coset graphs to construct small regular and biregular graphs,
Discrete Mathematics 347 (5), 2024.

R. Jajcay, J. Siran and Y. Wang, Generalized Cayley maps and their Petrie duals,
Ars Math. Contemp. 24, No. 3, Paper No. 1, 19 p. (2024)

G. Exoo, R. Jajcay and T. Raiman, On decreasing the orders of (k,g)-graphs,
Journal of Combinatorial Optimization, 2023, 46(4), 26

L. Eze, R. Jajcay and D. Mihalova, An algorithmic approach to determining spectra of orders of (k,g)-graphs,
ITAT 2023 Proceedings, CEUR Workshop Proceedings Vol. 3498 (2023) 204 - 208.

R. Jajcay and F. Moftakhar, Computer aided constructions of cages,
RIMS, Kokyuroku 9 (2022), 64 - 73.

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).

R. Jajcay, P. Potocnik and Stephen E. Wilson, Half-cyclic, dihedral and half-dihedral codes,
J. of Applied Mathematics and Computing 64 (2020), 691-708.

K. Jasencakova, R. Jajcay and T. Pisanski, A new generalization of generalized Petersen graphs,
The Art of Discrete and Applied Mathematics 3 (2020) #P1.04

I. Gutman, S. Filipovski and R. Jajcay, Variations on McClelland's bound for graph energy,
Discrete Math. Lett. 3 (2020), 57-60.

S. Filipovski and R. Jajcay, New upper bounds for the energy and spectral radius of graphs,
MATCH Commun. Math. Comput. Chem. 84 (2020), 335-343.

R. Jajcay, C.-H. Li, J. Siran and Y. Wang, Regular and orientably-regular maps with quasiprimitive automorphism groups on vertices,
Geometriae Dedicata 203 (2019), 389-418.

R. Jajcay and T. Jajcayova, k-hypergraphs with regular automorphisms groups,
Acta Math. Univ. Comenianae 88 (3) (2019), 835-840.

R. Jajcay, P. Potocnik and S. Wilson, The Praeger-Xu graphs: Cycle structures, maps and semitransitive orientations,
Acta Math. Univ. Comenianae 88 (2) (2019), 269-291.

S. Filipovski, A. Ramos Rivera and R. Jajcay, On biregular bipartite graphs of small excess,
Discrete Math. 342 (2019), 2066-2076.

E. Eiben, R. Jajcay and P. Sparl, Symmetry properties of generalized graph truncations,
J. of Comb. Theory, Ser. B 137 (2019), 291-315.

R. Jajcay, S. Miklavic, P. Sparl and G. Vasiljevic, On certain edge-transitive bicirculants,
Electron. J. of Comb. 26 (2) (2019) #P2.6

R. Jajcay and G.A. Jones, r-regular families of graph automorphisms,
Europ. J. of Comb. 79 (2019), 97-110.

G. Exoo, R. Jajcay, M. Macaj and J. Siran, On the defect of vertex-transitive graphs of given degree and diameter,
J. Comb. Theory, Series B, 134 (2019), 322-340.

S. Filipovski and R. Jajcay, On the non-existence of families of (d,k,delta)-digraphs containing only selfrepeat vertices,
Linear Algebra and its Applications 563, (2019), 302-312.

R. Jajcay, T. Jajcayova and M. Opial, Enumeration of matrices with prohibited bounded sub-windows,
ITAT 2018 Proceedings, CEUR Workshop Proceedings Vol. 2203 (2018).

R. Jajcay, Gy. Kiss and S. Miklavic, Edge-girth-regular graphs,
Europ. J. of Comb. 72, (2018), 70-82.

S. Filipovski and R. Jajcay, On the excess of vertex-transitive graphs with given degree and girth,
Discrete Math. 341, No. 3, 772-780 (2018).

M. Bachraty and R. Jajcay, Classification of coset-preserving skew-morphisms of finite cyclic groups,
Australasian Journal of Combinatorics, Vol. 67 (2) (2017), 259-280.

T.B. Jajcayova, S. Filipovski and R. Jajcay, Counting cycles in graphs with small excess,
Lecture Notes of Seminario Interdisciplinare di Matematica Vol. 14 (2016), 17-36.

G.A. Jones and R. Jajcay, Cayley properties of merged Johnson graphs,
Journal of Algebraic Combinatorics 44 (2016), 1047-1067.

T.B. Jajcayova, S. Filipovski and R. Jajcay, Improved lower bounds for the orders of even-girth cages,
The Electronic Journal of Combinatorics 23(3) (2016), #P3.55.

M. Bachraty and R. Jajcay, Powers of skew-morphisms,
in Symmetries in Graphs, Maps, and Polytopes, 5th SIGMAP Workshop, West Malvern, UK, July 2014 (J. Siran and R. Jajcay, ed.),
Springer Proceedings in Mathematics & Statistics 159 (2016), 1-26.

G. Exoo and R. Jajcay, Biregular cages of odd girth,
J. Graph Theory 81, No. 1 (2016), 50-56.

G. Araujo-Pardo, G. Exoo and R. Jajcay, Small biregular graphs of even girth,
Discrete Math. 339, No. 2 (2016), 658-667.

M. Conder, R. Jajcay, and T. Tucker, Cyclic complements and skew morphisms of groups,
J. Algebra 453 (2016), 68-100.

R. Jajcay and R. Nedela, Half-regular Cayley maps,
Graphs and Combinatorics 31 (2015) 1003-1018.

M. Boben, R. Jajcay and T. Pisanski, Generalized cages,
The Electronic Journal of Combinatorics 22(1) (2015), #P1.77.

G. Exoo, R. Jajcay and J. Siran, Cayley cages,
J. Algebr. Comb. Volume 38, Issue 1 (2013) 209-224.

G. Exoo and R. Jajcay, Recursive constructions of small regular graphs of given degree and girth,
Discrete Mathematics 312 (2012) 2612-2619.

R. Jajcay and J. Siran, Small vertex-transitive graphs of given degree and girth,
Ars Mathematica Contemporanea 4 (2011) 375-384.

R.-Q. Feng, R. Jajcay and Y. Wang, Regular t-balanced Cayley maps for abelian groups,
Discrete Math. 311 (2011) 2309-2316.

G. Exoo and R. Jajcay, On the girth of voltage graph lifts,
Europ. J. of Combinatorics 32 (2011) 554-562.

M. Conder, G. Exoo and R. Jajcay, On the limitations of the use of solvable groups in Cayley graph cage constructions,
Europ. J. of Combinatorics 31 (2010), 1819-1828.

T.B. Jajcayova, R. Jajcay, and E.S. Kramer, The life and mathematics of Dale Marsh Mesner, 1923 - 2009,
Bulletin of the ICA 59 (2010) 9-30.

G. Exoo and R. Jajcay, Properties of Groups for the Cage and Degree/Diameter Problems,
Electronic Notes in Discrete Mathematics 34 (2009) 341-345.

G. Exoo and R. Jajcay, Dynamic cage survey,
Electron. J. Combin., Dynamic Survey 16, September 2008.

M. Conder, R. Jajcay, and T. Tucker, Regular Cayley maps for finite abelian groups,
J. Algebr. Comb. 25, No. 3, 259-283 (2007).

M. Conder, R. Jajcay, and T. Tucker, Regular t-balanced Cayley maps,
J. Comb. Theory, Ser. B 97, No. 3, 453-473 (2007).

R. Jajcay, A. Malnic, and D. Marusic, Counting closed oriented walks in vertex-transitive graphs,
Discrete Math. 307, No. 3-5, 484-493 (2007).

R. B. Richter, R. Jajcay, J. Siran, T.W. Tucker, and M.E. Watkins, Cayley maps,
J. Combin. Theory Ser. B, 95 (2005), no. 2, 189 - 245.

D. Archdeacon, D. Froncek, R. Jajcay, Z. Ryjacek and J. Siran, Regular clique covers of graphs ,
Australas. J. of Combin. 27 (2003), 307--316.

T.B. Jajcayova and R. Jajcay, On the contributions of D.M. Mesner ,
Bull. Inst. Combin. Appl 36 (2002), pp. 46--52.

R. Jajcay and J. Siran, Skew-morphisms of regular Cayley maps ,
Discrete Math. 244 (2002), no 1-3, 167-179.

R. Jajcay, Representing finite groups as regular automorphism groups of combinatorial
structures, Ars Combinatoria 62 (2002), pp. 51-64.

R. Jajcay, The structure of automorphism groups of Cayley graphs and maps,
Journal of Algebraic Combinatorics 12 (2000), 73-84

T.B. Jajcayova and R. Jajcay, Notes on subtractive properties of natural numbers,
Bulletin of the ICA, 25 (1999), 29-40.

R. Jajcay and C. H. Li, Constructions of self-complementary circulants
with no multiplicative isomorphisms, Eur. J. Comb. 22, no. 8, 1093-1100.

R. Jajcay and D. Mesner, Embedding arbitrary finite simple graphs into small
strongly regular graphs, J. Graph Theory 34 (2000), no.1., 1--8

L. G. Chouinard II., R. Jajcay and S. S. Magliveras, Finite groups, in Handbook of
Combinatorial Design (C. Colbourn and J. Dinitz, ed.), CRC Press (1996), 587-614.

R. Jajcay and J. Siran, More constructions of vertex-transitive non-Cayley graphs
based on counting closed walks, Australasian J. of Comb. 14 (1996), 121-132.

R. Jajcay, Characterization and construction of Cayley graphs admitting regular
Cayley maps, Discrete Mathematics 158 (1996), 151-160.

R. Jajcay, On a construction of infinite families of regular Cayley maps,
Combinatorica 18 (2) (1998) 191-199

R. Jajcay and J. Siran, A construction of vertex-transitive non-Cayley graphs,
Australasian J. of Combin. 10 (1994), 105-114.

R. Jajcay, On a new product of groups, Europ. J. of Combinatorics 15 (1994),
251-252.

O. Grosek and R. Jajcay, Difference sets on an infinite cyclic semigroup,
JCMCC, 13, (1993), 167-174.

R. Jajcay, Automorphism groups of Cayley maps, Journal of Comb. Theory
Series B 59 (1993), 297-310.

R. Jajcay, Enumeration of border matrices, Matematicke obzory, zv. 31,
(1989), 41-49.

R. Jajcay, Estimates of the number of vector fields on Grassmannians,
RNDr-thesis at the Comenius University, (1988).


R. Jajcay and T. Jajcayova, The Mathematics of Various Entertaining Subjects: Research in Recreational Math, edited by Jennifer Beineke and Jason Rosenhouse,
a review for the London Mathematical Society Newsletter, April 2016.

R. Jajcay and T. Jajcayova, Mathema: an interactive book for iPad, by Hugo Parlier and Paul Turner,
a review for the London Mathematical Society Newsletter, October 2015.

R. Jajcay and T. Jajcayova, Really big numbers, by Richard Evan Schwartz,
a review for the London Mathematical Society Newsletter, November 2014.


J. Siran, R. Jajcay (Eds.), Symmetries in Graphs, Maps, and Polytopes, 5th SIGMAP Workshop, West Malvern, UK, July 2014,
Springer Proceedings in Mathematics & Statistics 159 (2016).


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



Reviewer for Zentralblatt fur Mathematik and Mathematical Reviews


Refereed textbooks on Numerical Methods in C, Number Theory, Mathematical Reasoning,
Differential Equations, Algebra and Trigonometry, and Discrete Mathematics


Refereed for Graphs and Combinatorics, JCMCC, J. of Combinatorics, Electronic J. of Comb.,
J. of Comb. Design, Australasian J. of Comb., Ars Combinatoria, J. of Graph Th.,
J. of Comb. Th. B, Information and System Sciences, Discrete Math., European J. of Comb.,
Tatra Mountains Math. J., Mathematica Slovaka, , Acta Mathematica Sinica,
Ars Mathematica Contemporanea and Information Sciences


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