Prof Tomas Vetrik
Position
Professor
Department
Mathematics and Applied Mathematics
Address
MATHEMATICS AND APPLIED MATHEMATICS
IB 74
UFS
Telephone
051/401-2912
Office
Mathematical Sciences Building 110
Information

Short CV

January 2020 - present
Professor, University of the Free State, Bloemfontein, South Africa

March 2014 - December 2019
Associate Professor, University of the Free State, Bloemfontein, South Africa

September 2012 - February 2014 
Lecturer, University of Pretoria, Pretoria, South Africa

April 2010 - August 2012 
Postdoctoral researcher, University of KwaZulu-Natal, Durban, South Africa

October 2007 - January 2009 
Researcher, Slovak University of Technology, Bratislava, Slovakia

June 2008 - September 2008 
Postdoctoral researcher, Bandung Institute of Technology, Bandung, Indonesia

October 2004 - June 2008 
PhD study in applied mathematics, Slovak University of Technology, Bratislava, Slovakia

March 2006 - May 2006 
PhD research stay, Vienna University of Technology, Vienna, Austria

September 2004 - December 2005 
Teaching assistant, University of Trencin, Trencin, Slovakia

May 2005 
PhD study stay, University of Ostrava, Ostrava, Czech Republic

September 1999 - May 2004 
MSc and BSc study in mathematics, Constantine the Philosopher University, Nitra, Slovakia

Publications

1. M. R. Alfuraidan, K. C. Das, T. Vetrik, S. Balachandran: General sum-connectivity index of unicyclic graphs with given diameter, Discrete Applied Mathematics 295 (2021), 39 – 46.
2. M. R. Alfuraidan, S. Balachandran, T. Vetrik: General multiplicative Zagreb indices of unicyclic graphs, Carpathian Journal of Mathematics 37, No. 1 (2021), 1 – 11.
3. S. Balachandran, T. Vetrik: Exponential second Zagreb index of chemical trees, Transactions on Combinatorics 10, No. 2 (2021), 25 – 34.
4. H. Deng, T. Vetrik, S. Balachandran: On the harmonic index and the signless Laplacian spectral radius of graphs, Kragujevac Journal of Mathematics 45, No. 2 (2021), 299 – 307.
5. T. Vetrik, M. Masre: General eccentric connectivity index of trees and unicyclic graphs, Discrete Applied Mathematics 284 (2020), 301 – 315.
6. T. Vetrik, S. Balachandran: General multiplicative Zagreb indices of trees and unicyclic graphs with given matching number, Journal of Combinatorial Optimization 40 (2020), 953 – 973.
7. M. Abas, T. Vetrik:  Metric dimension of directed Cayley graphs of metacyclic groups, Theoretical Computer Science 809 (2020), 61 – 72.
8. M. R. Alfuraidan, M. Imran, M. K. Jamil, T. Vetrik: General multiplicative Zagreb indices of graphs with bridges, IEEE Access 8 (2020), 118725 – 118731.
9. T. Vetrik: On the metric dimension of directed and undirected circulant graphs, Discussiones Mathematicae Graph Theory 40 (2020), 67 – 76.
10. H. Deng, T. Vetrik, S. Balachandran: On the harmonic index and diameter of unicyclic graphs, Mathematical Reports 22 (2020), 11 – 18.
11. M. R. Alfuraidan, T. Vetrik, S. Balachandran: General multiplicative Zagreb indices of graphs with a small number of cycles, Symmetry 12 (2020), 514.
12. T. Vetrik: General formula for degree-based topological indices of titania nanotubes, U.P.B. Scientific Bulletin, Series B 82, No. 4 (2020), 125 – 132.
13. M. Masre, S. A. Fufa, T. Vetrik: Distance-based indices of complete m-ary trees, Discrete Mathematics, Algorithms and Applications 12, No. 4 (2020), 2050041.
14. J. P. Mazorodze, S. Mukwembi, T. Vetrik: Gutman index, edge-Wiener index and edge-connectivity, Transactions on Combinatorics 9, No. 4 (2020), 231 – 242.
15. T. Vetrik: Degree-based topological indices of TUC4C8(S) nanotubes, U.P.B. Scientific Bulletin, Series B 81, No. 4 (2019), 187 – 196.
16. M. S. Bataineh, M. M. M. Jaradat, T. Vetrik: Edge-maximal graphs without disjoint odd cycles, Ars Combinatoria 143 (2019), 247 – 253.
17. D. A. Mengesha, T. Vetrik: Resolving sets of directed Cayley graphs for the direct product of cyclic groups, Czechoslovak Mathematical Journal 69, No. 3 (2019), 621 – 636.
18. T. Vetrik, S. Balachandran: General multiplicative Zagreb indices of graphs with given clique number, Opuscula Mathematica 39, No. 3 (2019), 433 – 446.
19. L. du Toit, T. Vetrik: On the metric dimension of circulant graphs with 2 generators, Kragujevac Journal of Mathematics 43, No. 1 (2019), 49 – 58. 
20. T. Vetrik: Polynomials of degree-based topological indices for hexagonal nanotubes, U.P.B. Scientific Bulletin, Series B 81, No. 1 (2019), 109 – 120.
21. T. Vetrik, S. Balachandran: General multiplicative Zagreb indices of trees, Discrete Applied Mathematics 247 (2018), 341 – 351.
22. P. Ali, P. Dankelmann, M. J. Morgan, S. Mukwembi, H. Swart, T. Vetrik: The average eccentricity, spanning trees of plane graphs, size and order, Utilitas Mathematica 107 (2018), 37 – 49.
23. E. Maritz, T. Vetrik: The partition dimension of circulant graphs, Quaestiones Mathematicae 41, No. 1 (2018), 49 – 63.
24. T. Vetrik: On bipartite Cayley graphs of small diameter, Mathematical Reports 20, No. 70 (2018), 171 – 176.
25. T. Vetrik: Degree-based topological indices of hexagonal nanotubes, Journal of Applied Mathematics and Computing 58, No. 1 (2018), 111 – 124.
26. T. Vetrik: The Randic index and the redefined Zagreb index of titania nanotubes TiO2 [m,n], U.P.B. Scientific Bulletin, Series B 80, No. 1 (2018), 157 – 162.
27. M. M. M. Jaradat, M. S. Bataineh, T. Vetrik, A. M. M. Rabaiah: A note on the Ramsey numbers for theta graphs versus the wheel of order 5, AKCE International Journal of Graphs and Combinatorics 15, No. 2 (2018), 187 – 189.
28. M. S. Bataineh, T. Vetrik, M. M. M. Jaradat, A. M. M. Rabaiah: The Ramsey number for two graphs of order 5, Journal of Discrete Mathematical Sciences and Cryptography 21 (2018), 1523 – 1528.
29. M. Abas, T. Vetrik: Large Cayley digraphs and bipartite Cayley digraphs of odd diameter, Discrete Mathematics 340 (2017), 1162 – 1171.
30. P. Mafuta, S. Mukwembi, S. Munyira, T. Vetrik: Hamiltonicity, minimum degree and leaf number, Acta Mathematica Hungarica 152 (2017), 217 – 226.
31. T. Vetrik: On the metric dimension of circulant graphs with 4 generators, Contributions to Discrete Mathematics 12 (2017), 104 – 114.
32. P. Dankelmann, E. Jonck, T. Vetrik: The degree-diameter problem for outerplanar graphs, Discussiones Mathematicae Graph Theory 37 (2017), 823 – 834.
33. T. Vetrik: The metric dimension of circulant graphs, Canadian Mathematical Bulletin 60 (2017), 206 – 216.
34. S. Dorfling, E. C. M. Maritz, J. Smit, T. Vetrik: Non-proper edge-colouring of graphs and hereditary graph properties, Quaestiones Mathematicae 40 (2017), 539 – 551.
35. T. Vetrik, A. Ahmad: Computing the metric dimension of the categorial product of some graphs, International Journal of Computer Mathematics 94 (2017), 363 – 371.
36. P. Ali, J. P. Mazorodze, S. Mukwembi, T. Vetrik: On size, order, diameter and edge-connectivity of graphs, Acta Mathematica Hungarica 152 (2017), 11 – 24.
37. J. P. Mazorodze, S. Mukwembi, T. Vetrik: The Gutman index and the edge-Wiener index of graphs with given vertex-connectivity, Discussiones Mathematicae Graph Theory 36 (2016), 867 – 876.
38. S. Dorfling, T. Vetrik: Edge-colouring of graphs and hereditary graph properties, Czechoslovak Mathematical Journal 66 (2016), 87 – 99.
39. S. Mukwembi, T. Vetrik: On the radius of neighborhood graphs, Quaestiones Mathematicae 39 (2016), 577 – 585.
40. T. Vetrik: Diameter of neighborhood graphs, Bulletin of the Malaysian Mathematical Sciences Society 39 (2016), 117 – 122.
41. J. P. Mazorodze, S. Mukwembi, T. Vetrik: On the Gutman index and minimum degree, Discrete Applied Mathematics 173 (2014), 77 – 82.   
42. P. Dankelmann, T. Vetrik: The degree-diameter problem for claw-free graphs and hypergraphs, Journal of Graph Theory 75 (2014), 105 – 123.
43. T. Vetrik: Abelian Cayley graphs of given degree and diameter 2 and 3, Graphs and Combinatorics 30 (2014), 1587 – 1591.
44. I. Broere, T. Vetrik: Universal graphs for two graph properties, Ars Combinatoria 116 (2014), 257 – 262.
45. S. Mukwembi, T. Vetrik: Wiener index of trees of given order and diameter at most 6, Bulletin of the Australian Mathematical Society 89 (2014), 379 – 396.
46. T. Vetrik: Cayley graphs of given degree and diameters 3, 4 and 5, Discrete Mathematics 313 (2013), 213 – 216.
47. T. Vetrik: Large Cayley digraphs of given degree and diameter, Discrete Mathematics 312 (2012), 472 – 475.
48. T. Vetrik: List coloring of complete multipartite graphs, Discussiones Mathematicae Graph Theory 32 (2012), 31 – 37.
49. T. Vetrik, R. Simanjuntak, E. Baskoro: Large bipartite Cayley graphs of given degree and diameter, Discrete Mathematics 311 (2011), 324 – 326.
50. H. Macbeth, J. Siagiova, J. Siran, T. Vetrik: Large Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter, Journal of Graph Theory 64, No. 2 (2010), 87 – 98.
51. T. Vetrik, L. Yulianti, E. Baskoro: On Ramsey $(K_{1,2},C_4)$-minimal graphs, Discussiones Mathematicae Graph Theory 30 (2010), 637 – 649.
52. T. Vetrik: An upper bound for graphs of diameter 3 and given degree obtained as Abelian lifts of dipoles, Discussiones Mathematicae Graph Theory 28 (2008), 91 – 96.
53. E. Baskoro, T. Vetrik, L. Yulianti: A note on Ramsey $(K_{1,2}, C_4)$-minimal graphs of diameter 2, International Conference 70 Years of FCE STU (2008), 1 – 4.
54. J. Siagiova, T. Vetrik: Large vertex-transitive and Cayley graphs with given degree and diameter, Electronic Notes in Discrete Mathematics 28 (2007), 365 – 369.
55. T. Vetrik: Factorization of complete graphs into three factors with the smallest diameter equal to 3 or 4, Australasian Journal of Combinatorics 39 (2007), 183 – 190.
56. T. Vetrik: Diameter in walk graphs, Acta Mathematica Universitatis Comenianae 76 (2007), 223 – 230.
57. T. Vetrik: A note on factorization of complete graphs, Journal of Electrical Engineering 57 (2006), 99 – 100.
58. T. Vetrik: Decompositions of complete graphs into three factors, Journal of Electrical Engineering 56 (2005), 113 – 114.

Publications (Short List)


Research

Conference presentations:

  1. T. Vetrik, S. Balachandran: General multiplicative Zagreb indices of trees, 41st Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, Rotorua, New Zealand, December 10 – 14, 2018.
  2. T. Vetrik: Graphs of given degree and diameter, International Conference on Discrete Mathematics and Data Sciences ICDMDS‘18, Thanjavur, India, September 28 – 29, 2018. (keynote lecture)
  3. T. Vetrik: The metric dimension and the partition dimension of circulant graphs, 8th International Conference on Research and Education in Mathematics, Bandung, Indonesia, August 11 - 13, 2017.
  4. T. Vetrik: Selected topics in the extremal graph theory, 13th Mathematical Conference in Nitra, Nitra, Slovakia, June 18 - 19, 2015. (invited lecture)
  5. M. Abas, T. Vetrik: Directed Cayley graphs of given degree and diameter, The Second Gdansk Workshop on Graph Theory, Gdansk, Poland, June 26 - 28, 2014.
  6. T. Vetrik: K-bases of groups and Cayley graphs, South African Mathematical Society. 56th Annual Congress, Pietermaritzburg, South Africa, October 30 - November 1, 2013.
  7. T. Vetrik: Large Cayley graphs of given degree and diameter 3, 4 and 5, South African Mathematical Society. 55th Annual Congress, Stellenbosch, South Africa, October 30 - November 2, 2012.
  8. T. Vetrik, P. Dankelmann, D. Erwin, S. Mukwembi: Inverse degree of a graph of given order and size, Joint Congress of the South African and American Mathematical Societies, Port Elizabeth, South Africa, November 29 - December 3, 2011.
  9. T. Vetrik, P. Dankelmann: The degree-diameter problem for claw-free graphs and hypergraphs, 23rd British Combinatorial Conference, Exeter, Great Britain, July 3-8, 2011.
  10. T. Vetrik, P. Dankelmann: Large claw-free graphs of given degree and diameter, South African Mathematical Society, 53rd Annual Congress, Pretoria, South Africa, November 3-5, 2010.
  11. E. Baskoro, T. Vetrik, L. Yulianti: A note on Ramsey $(K_{1,2},C_4)$-minimal graphs of diameter 2, International Conference 70 Years of FCE STU, Bratislava, Slovakia, December 4-5, 2008.
  12. T. Vetrik: Large Cayley graphs of given degree and diameter, National Mathematics Conference XIV, Palembang, Indonesia, July 24-27, 2008.
  13. T. Vetrik: Choosability of complete multipartite graphs, 42nd Czech-Slovak Conference on Graph Theory – Graphs 2007, Hradec nad Moravicí, Czech Republic, June 11-15, 2007.
  14. T. Vetrik: Large vertex-transitive and Cayley graphs with given degree and diameter, 6th Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, Prague, Czech Republic, July 10-15, 2006.
  15. T. Vetrik: Factorization of Complete Graphs, International Conference in Applied Mathematics ISCAM 2006, Bratislava, Slovakia, April 7-8, 2006.
  16. T. Vetrik: Decompositions of Graphs, 40th Czech-Slovak Conference on Graph Theory – Graphs 2005, Budmerice, Slovakia, May 30 - June 3, 2005.
  17. T. Vetrik: Decompositions of Complete Graphs, International Conference in Applied Mathematics ISCAM 2005, Bratislava, Slovakia, April 15-16, 2005.

Area(s) of Interest


Courses Presented

1st semester 2018, 2019, 2020 and 2021: 
Discrete Mathematics: course for 3rd year students, 
University of the Free State, Bloemfontein, South Africa

2nd semester 2014, 2015, 2017, 2018, 2019 and 1st semester 2021: 
Coding Theory: course for postgraduate students, 
University of the Free State, Bloemfontein, South Africa

1st semester 2014 and 2017: 
Graph Theory: course for postgraduate students, 
University of the Free State, Bloemfontein, South Africa

2nd semester 2013: 
Calculus II: course for 1st year engineering students, 
University of Pretoria, Pretoria, South Africa

1st semester 2013 and 2014: 
Mathematics I: course for 1st year science students, 
University of Pretoria, Pretoria, South Africa

1st semester 2012: 
Mathematics for the Natural Science: course for 1st year students, 
University of KwaZulu-Natal, Durban, South Africa

1st semester 2011: 
Linear Algebra and Coding Theory: course for 3rd year science students, 
University of KwaZulu-Natal, Durban, South Africa

2nd semester 2007 and 2008: 
Mathematics III: course for 2nd year students of the Faculty of Civil Engineering, 
Slovak University of Technology, Bratislava, Slovakia

2nd semester 2007 and 2008, 1st semester 2008: 
Mathematics I: course for 1st year students of the Faculty of Civil Engineering, 
Slovak University of Technology, Bratislava, Slovakia

1st semester 2008: 
Mathematics II: course for 1st year students of the Faculty of Civil Engineering, 
Slovak University of Technology, Bratislava, Slovakia

2nd semester 2007: 
Mathematics I: course for 1st year students of the Faculty of Architecture, 
Slovak University of Technology, Bratislava, Slovakia

2nd semester 2004 and 2005, 1st semester 2005: 
Tutoring courses for undergraduate students, 
Slovak University of Technology, Bratislava, Slovakia

2nd semester 2004 and 2005, 1st semester 2005: 
Tutoring courses for undergraduate students, 
University of Trencin, Trencin, Slovakia

Community Service


Service Learning

I presented lectures at research seminars at the following universities: 

  1. Yeungnam University, Gyeongsan, South Korea (July 2019)
  2. King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia (November 2018: two talks, April 2017)
  3. United Arab Emirates University, Al Ain, United Arab Emirates (February 2018)
  4. Addis Ababa University, Addis Ababa, Ethiopia (October 2017)
  5. Bandung Institute of Technology, Bandung, Indonesia (August 2017, June 2008)
  6. University of the Free State, Bloemfontein, South Africa (February 2017)
  7. University of Dar es Salaam, Dar es Salaam, Tanzania (October 2016)
  8. University of Costa Rica, San Jose, Costa Rica (June 2016)
  9. Costa Rica Institute of Technology, Cartago, Costa Rica (June 2016)
  10. University of the Philippines, Baguio, Philippines (June 2015)
  11. Qatar University, Doha, Qatar (November 2014)
  12. Nelson Mandela Metropolitan University, Port Elizabeth, South Africa (April 2014)
  13. University of Pretoria, Pretoria, South Africa (September 2012)
  14. University of Zimbabwe, Harare, Zimbabwe (March 2012)
  15. University of Andalas, Padang, Indonesia (February 2012)
  16. University of Malaya, Kuala Lumpur, Malaysia (January 2012)
  17. University of KwaZulu-Natal, Durban, South Africa (4 talks: September 2011, March 2011, September 2010, July 2010)
  18. Sepuluh Nopember Institute of Technology, Surabaya, Indonesia (August 2008)
  19. University of Brawijaya, Malang, Indonesia (August 2008)
  20. Airlangga University, Surabaya, Indonesia (August 2008)
  21. Comenius University, Bratislava, Slovakia (2 talks: April 2008, October 2007)
  22. Vienna University of Technology, Vienna, Austria (April 2006)
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