Professional page 

Martin Knor 

Slovenska verzia tejto stranky 

 


Teaching

I am a teacher at the Faculty of Civil Engineering of Slovak University of Technology. However, I have also some lectures on other schools. Here is a list of courses I had. (By bold I denote those, taught in the school year 2014/15.)

  1. Introductory course in geometry, Faculty of Civil Engineering, Slovak University of Technology (taught in English).
  2. Constructive geometry, Faculty of Civil Engineering, Slovak University of Technology (taught in English)(see syllabus).
  3. Algebraic structures and the logic, Faculty of Civil Engineering, Slovak University of Technology (taught in Slovak)(see syllabus).
  4. Theory of graphs, Faculty of Civil Engineering, Slovak University of Technology (taught in Slovak)(see syllabus).
  5. Linear and nonlinear optimization, Faculty of Civil Engineering, Slovak University of Technology (taught in Slovak)(see syllabus).
  6. Dynamic and stochastic optimization, Faculty of Civil Engineering, Slovak University of Technology (taught in Slovak).
  7. Mathematics II, Faculty of Civil Engineering, Slovak University of Technology (taught in English).
  8. Applied mathematics, Faculty of Civil Engineering, Slovak University of Technology (taught in Slovak).
  9. Theoretical background of raster graphics, Faculty of Civil Engineering, Slovak University of Technology (taught in Slovak).
  10. Mathematics for architects, Faculty of Architecture, Slovak University of Technology (taught in Slovak)(see syllabus).
  11. Mathematics for Managers I, Faculty of Management, Comenius University (taught in English)(see syllabus).
  12. Mathematics for Managers II, Faculty of Management, Comenius University (taught in English)(see syllabus).
  13. Mathematics for Managers III, Faculty of Management, Comenius University (taught in English).
  14. Introduction to discrete mathematics I (mathematical logic), Faculty of Mathematics, Physics and Informatics, Comenius University (taught in Slovak).
  15. Introduction to discrete mathematics II (combinatorics), Faculty of Mathematics, Physics and Informatics, Comenius University (taught in Slovak).
  16. Graph theory, Faculty of Mathematics, Physics and Informatics, Comenius University (taught in Slovak).
  17. Discrete and geometrical algorithms, Faculty of Mathematics, Physics and Informatics, Comenius University (taught in Slovak).

Research

My research interest is focussed onto Graph Theory. Most of my papers deal either with iterated line graphs or with embeddings of graphs on surfaces or with topological indices.

List of papers

  1. M. Knor, L. Niepel,L. Soltes, Centers in iterated line graphs, Acta Mathematica Universitatis Commenianae, LXI, 2, (1992), 237-241. (preprint)
  2. M. Knor, L. Niepel, L. Soltes, Centers in line graphs, Mathematica Slovaca, 43, (1993), 11-20. (preprint)
  3. M. Knor, Note on linear arboricity, Mathematica Slovaca, 44, (1994), 117-122. (preprint)
  4. M. Knor, Gray codes in graphs, Mathematica Slovaca, 44, (1994), 395-412. (preprint)
  5. F. Gliviak, M. Knor, L. Soltes, On radially maximal graphs, Australasian Journal of Combinatorics, 9, (1994), 275-284. (preprint)
  6. M. Knor, On the number of cycles in f-connected graphs, Acta Mathematica Universitatis Commenianae, vol. LXIII, 2, (1994), 315-321. (preprint)
  7. F. Gliviak, M. Knor, L. Soltes, Two-radially maximal graphs with special centers, Mathematica Slovaca, 45, (1995), 227-233. (preprint)
  8. F. Gliviak, M. Knor, On radially extremal digraphs, Mathematica Bohemica, 120, (1995), 41-55. (preprint)
  9. M. Knor, A note on the radius of iterated line graphs, Acta Mathematica Universitatis Commenianae, vol. LXIV, 2, (1995), 255-258. (preprint)
  10. L. Niepel, M. Knor, L. Soltes, Distances in iterated line graphs, Ars Combinatoria, 43, (1996), 193-202. (preprint)
  11. M. Knor, Characterization of minor-closed pseudosurfaces, Ars Combinatoria, 43, (1996), 246-256. (preprint)
  12. M. Knor, L. Niepel, Radii and centers in iterated line digraphs, Discussiones Mathematicae, Graph Theory, 16, (1996), 17-26. (preprint)
  13. M. Knor, A note on radially Moore digraphs, IEEE Transactions on Computers, 45, (1996), 381-383. (preprint)
  14. M. Knor, On Ramsey-type games for graphs, Australasian Journal of Combinatorics, 14, (1996), 199-206. (preprint)
  15. M. Knor, J. Siran, Extremal graphs of diameter 2 and given maximum degree, embeddable in a fixed surface, Journal of Graph Theory, 24, (1997), 1-8. (preprint)
  16. M. Knor, L. Niepel Histories in iterated line graphs, Zbornik z vyrocnej konferencie Stavebnej fakulty STU, Slovak Technical University, Bratislava, 1998, 201-210. (preprint)
  17. M. Knor, L. Niepel Animacia afinity a kolineacie, Proceedings of seminars on Computational Geometry´98, Kocovce, 7, 1998, 64-66. (preprint)
  18. M. Knor, L. Niepel, Centers in path graphs, Journal of Combinatorics Information and System Sciences (JCISS), 24, (1999), 79-86. (preprint)
  19. M. Knor, L. Niepel, Path, trail and walk graphs, Acta Mathematica Universitatis Commenianae, vol. LXVIII, (1999), 253-256. (preprint)
  20. M. Knor, L. Niepel, Connectivity of path graphs, Discussiones Mathematicae, Graph Theory, 20, 2000, 181-195. (preprint)
  21. M. Knor, L. Niepel, Diameter in iterated path graphs, Discrete Mathematics, 233, (2001), 151-161. (preprint)
  22. M. Knor, L. Niepel, Iterated line graphs, Mathematics, Geometry and their Applications, Kocovce, 2001, 92-95. (preprint)
  23. M. Knor, L. Niepel, Graphs isomorphic to their path graphs, Mathematica Bohemica, 127, (2002), 473-480. (preprint)
  24. M. Knor, L. Niepel, M. Malah, Connectivity of path graphs, Australasian Journal of Combinatorics, 25, (2002), 175-184. (preprint)
  25. M. Knor, L. Niepel, Connectivity of iterated line graphs, Discrete Applied Mathematics, 125, (2003), 255-266. (preprint)
  26. M. Knor, L. Niepel, Line graphs as models of fault-tolerant networks, Mathematics, Geometry and their Applications, Kocovce, 2003, 17-26. (preprint)
  27. M.J. Grannell, T.S. Griggs, M. Knor, Face two-colourable triangulations of K13, Journal of Combinatorial Mathematics and Combinatorial Computing, 47, (2003), 75-81. (preprint)
  28. M.J. Grannell, T.S. Griggs, M. Knor, M. Skoviera, A Steiner triple system which colours all cubic graphs, Journal of Graph Theory, 46, (2004), 15-24. (preprint)
  29. Grannell M.J., Griggs T.S., Knor M., Biembeddings of Latin squares and Hamiltonian decompositions, Glasgow Mathematical Journal, 46, (2004), 443-457. (preprint)
  30. M. Knor, L. Niepel, Independence number in path graphs, Computing and Informatics, 23, (2004), 179-187. (preprint)
  31. M.J. Grannell, T.S. Griggs, M. Knor, Regular Hamiltonian embeddings of the complete bipartite graph Kn,n in an orientable surface, Congressus Numerantium, 163, (2004), 197-205. (preprint)
  32. M.J. Grannell, T.S. Griggs, M. Knor, Biembeddings of symmetric configurations of triples, Mathematics, Geometry and their Applications, Kocovce, 2004, 106-112. (preprint)
  33. M. Knor, T. Madaras, On farness- and reciprocally-selfcentric antisymmetric graphs, Proceedings of the Thirty-Fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, 171, (2004), 173-178. (preprint)
  34. M. Knor, Minimal non-selfcentric radially-maximal graphs of radius 4, Mathematics, Geometry and their Applications, Kocovce, 2005, 85-86. (preprint)
  35. M.J. Grannell, T.S. Griggs, M. Knor, J. Siran, Triangulations of orientable surfaces by complete tripartite graphs, Discrete Mathematics, 306, (2006), 600-606. (preprint)
  36. T. Boehme, M. Knor, L. Niepel, Linkability in iterated line graphs, Discrete Mathematics, 306, (2006), 666-669. (preprint)
  37. M. Knor, L. Niepel, Distance independent domination in iterated line graphs, Ars Combinatoria, 79, (2006), 166-170. (preprint)
  38. M. Knor, L. Niepel, Iterated line graphs are maximally ordered, Journal of Graph Theory, 52, (2006), 171-180. (preprint)
  39. M. Knor, (k,l)-radii of Petersen graph, Mathematics, Geometry and their Applications, Kocovce, 2006, 11-16. (preprint)
  40. M.J. Grannell, T.S. Griggs, M. Knor, Biembeddings of Latin squares of side 8, Quasigroups and Related Systems, 15, (2007), 273-278. (preprint)
  41. M. Knor, Small radially Moore graphs, Mathematics, Geometry and their Applications, Kocovce, 2007, 59-62. (preprint)
  42. M. Knor, Minimal non-selfcentric radially-maximal graphs of radius 4, Discussiones Mathematicae, Graph Theory, 27, (2007), 603-610. (preprint)
  43. M. Knor, J. Siran, Regular hamiltonian embeddings of Kn,n and regular triangular embeddings of Kn,n,n, Discrete Mathematics, 308, (2008), 4796-4800. (preprint)
  44. M.J. Grannell, T.S. Griggs, M. Knor, A.R.W. Thrower, A census of the orientable biembeddings of Steiner triple systems of order 15, Australasian Journal of Combinatorics, 42, (2008), 253-259. (preprint)
  45. M.J. Grannell, T.S. Griggs, M. Knor, Biembeddings of symmetric configurations and 3-homogenous Latin trades, Commentationes Mathematicae Universitatis Carolinae, 49, (2008), 411-420. (preprint)
  46. M.J. Grannell, T.S. Griggs, M. Knor, Orientable biembeddings of Steiner triple systems of order 15, Journal of Combinatorial Mathematics and Combinatorial Computing, 68, (2009), 129-136. (preprint)
  47. L. Niepel, M. Knor, Domination in a digraph and in its reverse, Discrete Applied Mathematics, 157, (2009), 2973-2977. (preprint)
  48. M.J. Grannell, T.S. Griggs, M. Knor, On biembeddings of Latin squares, Electronic Journal of Combinatorics, 16, (2009), R106, 12pp. (preprint)
  49. M. Knor, Unicyclic radially-maximal graphs on the minimum number of vertices, Australasian Journal of Combinatorics, 45, (2009), 97-107. (preprint)
  50. M. Knor, S. Zhou, Diameter and connectivity of 3-arc graphs, Discrete Mathematics, 310, (2010), 37-42. (preprint)
  51. M.J. Grannell, M. Knor, Biembeddings of Abelian groups, Journal of Combinatorial Designs, 18, (2010), 71-83. (preprint)
  52. M.J. Grannell, M. Knor, A lower bound for the number of orientable triangular embeddings of some complete graphs, Journal of Combinatorial Theory, Series B, 100, (2010), 216-225. (preprint)
  53. M.J. Grannell, M. Knor, An enumeration of minimum genus orientable embeddings of some complete bipartite graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 73, (2010), 95-102. (preprint)
  54. M. Knor, Minimal non-selfcentric radially-maximal graphs of radii 4 and 5, Journal of Combinatorial Mathematics and Combinatorial Computing, 73, (2010), 237-243. (preprint)
  55. L. Niepel, M. Knor, Domination in the cross product of digraphs, Ars Combinatoria, 97, (2010), 271-279. (preprint)
  56. L. Niepel, M. Knor, Efficient open domination in digraphs, Australasian Journal of Combinatorics, 49, (2011), 195-202. (preprint)
  57. M. Knor, G. Xu, S. Zhou, A study of 3-arc graphs, Discrete Applied Mathematics, 159, (2011), 344-353. (preprint)
  58. M.J. Grannell, M. Knor, Biembeddings of Latin squares obtained from a voltage construction, Australasian Journal of Combinatorics, 51, (2011), 259-270. (preprint)
  59. M.J. Grannell, M. Knor, A construction for biembeddings of Latin squares, Electronic Journal of Combinatorics, 18(1), (2011), P190, 17pp. (preprint)
  60. M. Dutour-Sikiric, M. Knor, P. Potocnik, J. Siran, R. Skrekovski, Hyperbolic analogues of fullerenes on orientable surfaces, Discrete Mathematics, 312, (2012), 729-736. (preprint)
  61. M. Knor, P. Potocnik, R. Skrekovski, On a conjecture about Wiener index in iterated line graphs of trees, Discrete Mathematics, 312, (2012), 1094-1105. (preprint)
  62. M.J. Grannell, M. Knor, Biembedding Abelian groups with mates having transversals, Journal of Combinatorial Designs, 20, (2012), 81-88. (preprint)
  63. M.J. Grannell, M. Knor, On the number of triangular embeddings of complete graphs and complete tripartite graphs, Journal of Graph Theory, 69, (2012), 370-382. (preprint)
  64. M. Knor, P. Potocnik, R. Skrekovski, The Wiener index in iterated line graphs, Discrete Applied Mathematics, 160, (2012), 2234-2245. (preprint)
  65. M.J. Grannell, M. Knor, Biembeddings of metacyclic groups and triangulations of orientable surfaces by complete graphs, Electronic Journal of Combinatorics, 19(3), (2012), P29, 17pp. (preprint)
  66. M. Knor, Small radial Moore graphs of radius 3, Australasian Journal of Combinatorics, 54, (2012), 207-216. (preprint)
  67. M. Knor, P. Potocnik, Efficient domination in cubic vertex-transitive graphs, European Journal of Combinatorics, 33, (2012), 1755-1764. (preprint)
  68. M. Knor, P. Potocnik, R. Skrekovski, Wiener index of iterated line graphs of trees homeomorphic to H, Discrete Mathematics, 313, (2013), 1104-1111. (preprint)
  69. J. Govorcin, M. Knor, R. Skrekovski, Line graph operation and small worlds, Information Processing Letters, 113, (2013), 196-200. (preprint)
  70. M. Knor, P. Potocnik, A note on 2-subset-regular self-complementary 3-uniform hypergraphs, Ars Combinatoria, 111, (2013), 33-36. (preprint)
  71. M. Knor, P. Potocnik, R. Skrekovski, Wiener index of iterated line graphs of trees homeomorphic to the claw K1,3, Ars Mathematica Contemporanea, 6, (2013), 211-219. (preprint)
  72. V. Andova, M. Knor, P. Potocnik, R. Skrekovski, On a variation of Randic index, Australasian Journal of Combinatorics, 56, (2013), 61-75. (preprint)
  73. M.J. Grannell, M. Knor, Dihedral biembeddings and triangulations by complete and complete tripartite graphs, Graphs and Combinatorics, 29(4), (2013), 921-932. (preprint)
  74. M. Knor, R. Skrekovski, Deterministic self-similar models of complex networks based on very symmetric graphs, Physica A, 392, (2013), 4629-2637. (preprint)
  75. M. Knor, M. Macaj, P. Potocnik, R. Skrekovski, Trees T satisfying W(L3(T))=W(T), Filomat, 28:3, (2014), 551-556. (preprint)
  76. M. Knor, M. Macaj, P. Potocnik, R. Skrekovski, Complete solution of equation W(L3(T))=W(T) for the Wiener index of iterated line graphs of trees, Discrete Applied Mathematics, 171, (2014), 90-103. (preprint)
  77. M. Knor, P. Potocnik, R. Skrekovski, Relationship between the edge-Wiener index and the Gutman index of a graph, Discrete Applied Mathematics, 167, (2014), 197-201. (preprint)
  78. M. Knor, Smallest regular graphs of given degree and diameter, Discussiones Mathematicae, Graph Theory, 34, (2014), 187-191. (preprint)
  79. M. Knor, J. Siran, Smallest vertex-trasitive graphs of given degree and diameter, Journal of Graph Theory, 75, (2014), 137-149. (preprint)
  80. M. Knor, R. Skrekovski, Wiener index of generalized 4-stars and of their quadratic line graphs, Australasian Journal of Combinatorics, 58, (2014), 119-126. (preprint)
  81. M.J. Grannell, M. Knor, Rigid Steiner triple systems obtained from projective triple systems, Journal of Combinatorial Designs, 22, (2014), 279-290. (preprint)
  82. M. Knor, B. Luzar, R. Skrekovski, I. Gutman, On Wiener index of common neighborhood graphs, MATCH Commun. Math. Comput. Chem., 72, (2014), 321-332. (preprint)
  83. K. Hrinakova, M. Knor, R. Skrekovski, A. Tepeh, A congruence relation for the Wiener index of graphs with a tree-like structure, MATCH Commun. Math. Comput. Chem., 72, (2014), 791-806. (preprint)
  84. M. Knor, B. Luzar, R. Skrekovski, Sandwiching the (generalized) Randic index, Discrete Applied Mathematics, 181, (2015), 160-166. (preprint)
  85. M. Knor, R. Skrekovski, A. Tepeh, Balaban index of cubic graphs, MATCH Commun. Math. Comput. Chem., 73, (2015), 519-528. (preprint)
  86. M. Knor, R. Skrekovski, Wiener index of line graphs, In: Quantitative Graph Theory: Mathematical Foundations and Applications, 279-301, Discrete Math. Appl. (Boca Raton), CRC Press, Boca Raton, Fl, 2015. (preprint)
  87. M. Knor, R. Skrekovski, A. Tepeh, An inequality between the edge-Wiener index and the Wiener index of a graph, Applied Mathematics and Computation, 269, (2015), 714-721. (preprint)
  88. M. Knor, M. Verdian-Rizi Hyperbolic analogues of fullerenes with face-types (6,9) and (6,10), Discrete Mathematics, 339, (2016), 103-108. (preprint)
  89. M. Knor, R. Skrekovski, A. Tepeh, Some remarks on Wiener index of oriented graphs, Applied Mathematics and Computation, 273, (2016), 631-636. (preprint)
  90. M. Knor, R. Skrekovski, A. Tepeh, Mathematical aspects of Wiener index, Ars Mathematica Contemporanea, 11, (2016), 327-352. (preprint)
  91. M. Knor, R. Skrekovski, A. Tepeh, Digraphs with large maximum Wiener index, Applied Mathematics and Computation, 284, (2016), 260-267.
  92. M. Knor, J. Sys, Dominance in a Cayley digraph and in its reverse, Australasian Journal of Combinatorics, 65, (2016), 212-219.
  93. M. Knor, R. Skrekovski, A. Tepeh Orientations of graphs with maximum Wiener index, Discrete Applied Mathematics, 211, (2016), 121-129.
  94. M.J. Grannell, M. Knor, Pasch trades on the projective triple system of order 31, Journal of Combinatorial Mathematics and Combinatorial Computing, 96, (2016), 23-31.
  95. V. Andova, M. Knor, R. Skrekovski Distances on nanotubical structures, Journal of Mathematical Chemistry, 54, (2016), 1575-1584.
  96. M. Knor, J. Kranjc, R. Skrekovski, A. Tepeh, A search for the minimum value of Balaban index, Applied Mathematics and Computation, 286, (2016), 301-310.
  97. M. Bonamy, M. Knor, B. Luzar, A. Pinolu, R. Skrekovski, On the difference between the Szeged and the Wiener index, Applied Mathematics and Computation, 312, (2017), 202-213.
  98. M. Knor, J. Kranjc, R. Skrekovski, A. Tepeh, On the minimum value of sum-Balaban index, Applied Mathematics and Computation, 303, (2017), 203-210.
  99. M. Knor, R. Skrekovski, A. Tepeh, A note on accumulation points of Balaban index, MATCH Commun. Math. Comput. Chem., 78, (2017), 163-168.
  100. M. Knor, R. Skrekovski, A. Tepeh, Some bounds on Balaban index, In: Bounds in Chemical Graph Theory - Basics, MCM 19 University of Kragujevac, Kragujevac, 2017, 189-200.
  101. M. Knor, R. Skrekovski, A. Tepeh, Wiener index of digraphs, In: Bounds in Chemical Graph Theory - Advances, MCM 21 University of Kragujevac, Kragujevac, 2017, 141-153.
  102. M. Knor, R. Skrekovski, A. Tepeh, Sum-Balaban index and its properties, In: Proceedings of the 1st Croatian Combinatorial Days, September 2016, University of Zagreb, Zagreb, 2017, 41-52.
  103. V. Andova, M. Knor, R. Skrekovski Distance based indices in nanotubical graphs: part 1, Journal of Mathematical Chemistry, 56, (2018), 2801-2815.
  104. V. Andova, M. Knor, R. Skrekovski Distance based indices in nanotubical graphs: part 2, Journal of Mathematical Chemistry, 56, (2018), 3076-3088.
  105. K. Hrinakova, M. Knor, R. Skrekovski, On a conjecture about the ratio of Wiener index in iterated line graphs, The Art of Discrete and Applied Mathematics, 1, (2018) #P1.09.
  106. M. Knor, S. Majstorovic, R. Skrekovski, Graphs whose Wiener index does not change when a specific vertex is removed, Discrete Applied Mathematics, 238, (2018), 126-132.
  107. M. Knor, R. Skrekovski, A. Tepeh Mathematical aspects of Balaban index, MATCH Commun. Math. Comput. Chem., 79, (2018), 685-718.
  108. M. Knor, S. Majstorovic, R. Skrekovski, Graphs preserving Wiener index upon vertex removal, Applied Mathematics and Computation, 338, (2018), 25-32.
  109. M. Knor, S. Majstorovic, R. Skrekovski, Graphs preserving total distance upon vertex removal, Electronic Notes in Discrete Mathematics, 68, (2018), 107-112.
  110. M. Knor, R. Skrekovski, A. Tepeh, Convexity result and trees with large Balaban index, Applied Mathematics and Nonlinear Sciences, 3(2), (2018), 433-446.

List of books and textbooks

  1. M. Knor, Kombinatorika a teoria grafov I, Univerzita Komenskeho, Bratislava, 2000. /skripta/
  2. M. Knor, L. Niepel, Kombinatorika a teoria grafov II, Univerzita Komenskeho, Bratislava, 2000. /skripta/
  3. M. Knor, J. Kollar, Matematika pre architektov, Slovenska Technicka Univerzita, Bratislava, 2001. /skripta/
  4. M. Knor, Mathematics for Managers I, Univerzita Komenskeho, Bratislava, 2003. /skripta/
  5. M. Knor, Mathematics for Managers II, Univerzita Komenskeho, Bratislava, 2003. /skripta/
  6. M. Knor, Aplikovana matematika (optimalizacne metody), Slovenska Technicka Univerzita, Stavebna fakulta, Bratislava, 2004. /ucebnica/
  7. M. Knor, Matematicka logika a diskretne struktury, Slovenska Technicka Univerzita, Bratislava, 2008, http://www.stuba.sk (ISBN 978-80-227-2837-9). /skripta/
  8. M. Knor, Teoria grafov, Slovenska Technicka Univerzita, Bratislava, 2008, http://www.svf.stuba.sk (ISBN 978-80-227-2879-9). /skripta/
  9. M. Knor, Heawoodova hypoteza a blokove plany, Slovenska Technicka Univerzita, Bratislava, 2009 (ISBN 978-80-227-3034-1). /monografia/
  10. M. Knor, Linearna a nelinearna optimalizacia, Slovenska Technicka Univerzita, Bratislava, 2009 http://www.svf.stuba.sk (ISBN 978-80-227-3102-7). /skripta/
  11. M. Knor, Descriptive Geometry, Slovenska Technicka Univerzita, Bratislava, 2009 (ISBN 978-80-227-3152-2). /ucebnica/
  12. M. Knor, Uvod do matematickej logiky, Slovenska Technicka Univerzita, Bratislava, 2016 (ISBN 978-80-227-4656-4). /skripta/

Since 1988 I am participating at the Czech and Slovak conference in Graph Theory, that is organized every year at the end of May. Since 1988 I missed only three years.


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Professional page of Martin Knor
Last update: December 26th, 2018
E-mail: (knor@math.sk)