IPM Positions

Senior Associate Researcher, School of Mathematics (2006 - 2015 )

Past IPM Positions

Senior Associate Researcher, School of Mathematics (2003 - 2006) Associate Researcher (non-resident), School of Mathematics (2001 - 2003) Senior Associate Researcher, School of Mathematics (2000 - 2001) Associate Researcher (non-resident), School of Mathematics (1996 - 2000)

Non IPM Affiliations

Professor of Sharif University of Technology

Research Activities

A transversal of an n?n matrix is a collection of n cells, no two of which are in the same row or column. A transversal of a matrix is a latin transversal if no two of its cells contain the same element. Ryser conjectured that every latin square of odd order has a transversal. In this project we wish to obtain some results on this conjecture. A conjecture of Snevily asserts that, for any odd n, every k?k submatrix of the Cayle addition table of Zn contains a latin transversal. Dasgupta, Karolyi, Serra and Szegedy proved Snevily''''s Conjecture and conjectured that for any natural number n and every odd k every k?k submatrix of the Cayle addition table of Zn contains a latin transversal. In this project we obtain some results about the later conjecture. For instance we show that for any natural numbers k and m and for any 1 ? i1 < i2 < ? < ik ? n, there exists a natural c(k,m) such that if n ? c(k, m), then any submatrix induced on the rows i1,?,ik and every arbitrary k columns of the addition table of Zn contains a latin transversal. Also Brualdi conjectured that every latin square has a near transversal ( that is, a selection of n-1 entries from different rows, columns and symbols, where n is the order of square). A latin square of order n naturally defines a proper edge coloring for the complete bipartite graph Kn,n. A latin transversal is equivalent to the existence of a multicolored perfect matching in the edge coloring of Kn,n. We will prove some theorems on the edge coloring of complete graphs which are in concerned with latin transversals in latin squares. Also we investigate the existence of multicolored cycles in the edge colorings of complete graphs (Grant Number: 81050027).

Present Research Project at IPM

Ryser''''s Conjecture and its relation to multicolored Graphs

Related Papers

1.	S. Akbari and S. Zare (Joint with M. Kano) 0-sum and 1-sum flows in regular graphs Electron. J. Combin. 23 (2016), #P2.37  [abstract]

2.	S. Akbari (Joint with M. Aaghabali, M. Ariannejad, and Z. Tajfirouz) Fully indecomposable and nearly decomposable graphs Discrete Math. (Accepted) [abstract]

3.	S. Akbari (Joint with H. A. Tavallaee and S. Khalashi Ghezelahmad) Some results on the intersection graph of submodules of a module Math. Slovaca (Accepted) [abstract]

4.	S. Akbari (Joint with H. A. Tavallaee and S. Khalashi Ghezelahmad) On the complement of the intersection graph of submodules of a module J. Algebra Appl. 14 (2015), # 11 pages  [abstract]

5.	S. Akbari ( Joint with T. R. Jensen and M. Siggers) Decomposition of graphs intp trees, forests, and regular subgraphs Discrete Math. 338 (2015), 1322-1327  [abstract]

6.	G. Aalipour and S. Akbari On the Cayley graph of a commutative ring with respect to its zero-divisors Comm. Algebra (Accepted) [abstract]

7.	S. Akbari (Joint with M. Aaghabali, S. Friedland, K. Markstrom, and Z. Tajfirouz) Upper bounds on the number of perfect matchings and directed 2-factors in graphs with given number of vertices and edges European J. Combin. 45 (2015), 132-144  [abstract]

8.	S. Akbari (Joint with K. Ozeki, A. Rezaei, R. Rotabi, and S. Sabour) {0, 2}-degree free spanning forests in graphs Discrete Math. 338 (2015), 1226-1231  [abstract]

9.	S. Akbari and M. Ghanbari (Joint with K. Ozeki) The Chromatic index of a claw-free graph whose core has maximum degree 2 Graphs Combin. (2014), DOI: 10.1007/s00373-014-1417-1  [abstract]

10.	S. Akbari (Joint with M. Habibi, A. Majidinya, and R. Manaviyat) On the inclusion ideal graph of a ring Comm. Algebra (Accepted) [abstract]

11.	G. Aalipour and S. Akbari (Joint with N. Shajari) Laplacian spectral characterization of two families of trees Linear Multilinear Algebra 62 (2014), 965-977  [abstract]

12.	S. Akbari and S. Zare (Joint with F. Rahmati) Zero-sum magic labelings and null sets of regular graphs Electron. J. Combin. 21 (2014), #P2.17  [abstract]

13.	S. Akbari and R. Nikandish (Joint with B. Miraftab) A note on co-maximal ideal graph of commutative rings Ars Combin. (Accepted) [abstract]

14.	S. Akbari, D. Kiani and M. Mirzakhah The multiplicity of Laplacian eigenvalue two in unicyclic graphs Linear Algebra Appl. 445 (2014), 18-28  [abstract]

15.	S. Akbari (Joint with S. Khojasteh) Commutative rings whose cozero-divisor graphs are unicyclic or of bounded degree Comm. Algebra 42 (2014), 1594-1605  [abstract]

16.	G. Aalipour and S. Akbari Some properties of a Cayley graph of a commutative ring Comm. Algebra 42 (2014), 1582-1593  [abstract]

17.	S. Akbari and M. Behboodi (Joint with G. Aalipour, R. Nikandish, M.J. Nikmehr, and F. Shaveisi) The classification of the annihilating-ideal graph of a commutative ring Algebra Colloq. 21 (2014), 249-256  [abstract]

18.	S. Akbari , D. Kiani, F. Mohammadi and S. Moradi (Joint with F. Rahmati) An algebraic criterion for the choosability of graphs Graphs Combin. (Accepted) [abstract]

19.	S. Akbari (Joint with M. Aghabali, M. Ariannejad, and A. Madadi) Vector space generated by the multiplicative J. Algebra Appl. (Accepted) [abstract]

20.	S. Akbari and R. Nikandish (Joint with M. J. Nikmehr) Some results on the intersection graphs of ideals of rings J. Algebra Appl. 12 (2013), 13 pages  [abstract]

21.	S. Akbari and S. Zare (Joint with M. Kano) A generalization of 0-sum flows in graphs Linear Algebra Appl. 438 (2013), 3629-3634  [abstract]

22.	S. Akbari (Joint with S. Khojasteh) Some criteria for the finiteness of cozero-divisor graphs J. Algebra Appl. 12 (2013), 12 pages  [abstract]

23.	S. Akbari and R. Nikandish Some results on the intersection graph of ideals of matrix algebras Linear Multilinear Algebra (2013), DOI: 10.1080/03081087.2013.769101  [abstract]

24.	S. Akbari (Joint with M. Habibi, A. Majidinya, and R. Manaviyat) On the idempotent graph of a ring J. Algebra Appl. 12 (2013), 14 pages  [abstract]

25.	S. Akbari and M. R. Oboudi On the edge cover polynomial of a graph European J. Combin. 34 (2013), 297-321  [abstract]

26.	S. Akbari and E. Ghorbani (Joint with A. Mahmoodi) Nowhere-zero eigenvectors of graphs Linear Multilinear Algebra 61 (2013), 273-279  [abstract]

27.	A. Abdollahi and S. Akbari (Joint with H. Dorbidi and H. Shahverdi) Commutativity pattern of finite non-abelian p-groups determine their orders Comm. Algebra 41 (2013), 451-461  [abstract]

28.	S. Akbari, M. Chavooshi, M. Ghanbari and S. Zare The f-chromatic index of a graph whose f-core has maximum degree 2 Canad. Math. Bull. (Accepted) [abstract]

29.	S. Akbari (Joint with E. Estaji and M. R. Khorsandi) On the unit graph of a non-commutative ring Algebra Colloq. (Accepted) [abstract]

30.	S. Akbari and M. Ghanbari (Joint with M. Kano and M. J. Nikmehr) The chromatic index of a graph whose core has maximum degree 2 Electron. J. Combin. 19 (2012), #P58  [abstract]

31.	S. Akbari (Joint with A. Aflaki, K. J. Edwards, D. S. Eskandari, M. Jamaali, and H. Ravanbod) On harmonious colouring of trees Electron. J. Combin. 19 (2012), #P3  [abstract]

32.	S. Akbari, N. Ghareghani, G. B. Khosrovshahi and S. Zare A note on zero-sum 5-flows in regular graphs Electron. J. Combin. 19 (2012), #P7  [abstract]

33.	S. Akbari (Joint with J. Kim and A. Kostochka) Harmonious coloring of trees with large maximum degree Discrete Mathematics 312 (2012), 1633-1637  [abstract]

34.	S. Akbari and S. Qajar (Joint with M. Khatirinejad) A note on the Roman bondage number of planar graphs Graphs Combin. (2012), DOI 10.1007/s00373-011-1129-8  [abstract]

35.	S. Akbari and M. Aryapoor (Joint with M. Jamaali) Chromatic number and clique number of subgraphs of regular graph of matrix algebras Linear Algebra Appl. 436 (2012), 2419-2424  [abstract]

36.	S. Akbari and M. Ghanbari (Joint with A. Ahadi and A. Dehghan) On the difference between chromatic number and dynamic chromatic number of graphs Discrete Math. (2011), Doi: 10.1016/j.disc.2011.09.006  [abstract]

37.	G. Aalipour, S. Akbari, R. Nikandish and F. Shaveisi (Joint with M. J. Nikmehr) On the coloring of the annihilating-ideal graph of a commutative ring Discrete Math. (2011), Doi: 10.1016/j.disc.2011.10.020  [abstract]

38.	S. Akbari, M. Chavooshi, M. Ghanbari and S. Zare (Joint with D. Cariolaro) Some criteria for a graph to be class 1 Discrete Mathematics (2011), DOi: 10.1016/j.disc.2011.09.035  [abstract]

39.	S. Akbari (Joint with A. Aflaki, D. S. Eskandari, M. Jamaali, and H. Ravanbod) On the harmonious coloring of trees Ars Combin. (Accepted) [abstract]

40.	S. Akbari (Joint with H. A. Tavallaee, S. Khalashi Ghezelahmad) Intersection graph of submodules of a module J. Algebra Appl. (Accepted) [abstract]

41.	S. Akbari and M. Ghanbari (Joint with R. Manaviyat and S. Zare) On the lucky choice number of graphs Graphs Combin. (2011), DOI 10.1007/s00373-011-1112-4  [abstract]

42.	S. Akbari, G. B. Khosrovshahi and A. Mofidi Zero-sum flows in designs J. Combin. Des. 19 (2011), 355-364  [abstract]

43.	G. Aalipour, S. Akbari, R. Nikandish and F. Shaveisi (Joint with M. J. Nikmehr) Minimal prime ideals and cycles in annihilating-ideal graphs Rocky Mountain J. Math. (Accepted) [abstract]

44.	S. Akbari and E. Ghorbani (Joint with A. Mahmoodi) On edge star sets in trees Discrete Math. 311 (2011), 1172-1178  [abstract]

45.	S. Akbari (Joint with V. Liaghat and A. Nikzad) Colorful paths in vertex coloring of graphs Electron. J. Combin. (Accepted) [abstract]

46.	S. Akbari, E. Ghorbani and M. R. Oboudi (Joint with J. H. Koolen) On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs Electron. J. Combin. 17 (2010), #R115  [abstract]

47.	S. Akbari and M. Ghanbari (Joint with S. Jahanbekam) On the dynamic chromatic number of graphs Contemp. Math. (Accepted) [abstract]

48.	S. Akbari and M. R. Oboudi (Joint with S. Qajar) On the rational independence roots Contemp. Math. (Accepted) [abstract]

49.	S. Akbari and M. R. Oboudi (Joint with S. Alikhani and Y. H. Peng) On the zeros of domination polynomial of a graph Contemp. Math. (Accepted) [abstract]

50.	S. Akbari, E. Ghorbani and M. R. Oboudi (Joint with J. H. Koolen) A relation between the Laplacian and signless Laplacian eigenvalues of a graph J. Algebraic Combin. 32 (2010), 459-464  [abstract]

51.	S. Akbari (Joint with S. Alikhani and Y. Peng) Characterization of graphs using domination polynomials European J. Combin. (Accepted) [abstract]

52.	S. Akbari and M. Jamaali (Joint with M. N. Iradmusa) A note on edge coloring of graphs Ars Combin. (Accepted) [abstract]

53.	S. Akbari (Joint with A. Daemi, O. Hatami, A. Javanmard, and A. Mehrabian) Zero-sum flows in regular graphs Graphs Combin. (Accepted) [abstract]

54.	S. Akbari (Joint with A. Daemi, O. Hatami, A. Javanmard, and A. Mehrabian) Nowhere-zero unoriented flows in Hamiltonian graphs Bull. Austral. Math. Soc. (Accepted) [abstract]

55.	S. Akbari and D. Kiani (Joint with K. Hassani Monfared, M. Jamaali, and E. Khanmohammadi) On the existence of nowhere-zero vectors for linear transformations Bull. Aust. Math. Soc. (Accepted) [abstract]

56.	S. Akbari and M. Ghanbari (Joint with A. Doni, S. Jahanbekam, and A. Saito) List coloring of graphs with cycles of length divisible by a given integer Contemp. Math. (Accepted) [abstract]

57.	S. Akbari (Joint with G. Aalipour-Hafshejani and Z. Ebrahimi) On D-equivalence class of complete bipartite graphs Ars Combin. (Accepted) [abstract]

58.	S. Akbari and M. Jamaali (Joint with A. Mahmoody and S. A. Seyed Fakhari) On the size of graphs whose cycles have length divisible by a fixed integer Australas. J. Combin. (Accepted) [abstract]

59.	S. Akbari (Joint with M. Ghanbari and S. Jahanbekam) On the dynamic coloring of Cartesian product graphs Ars Combin. (Accepted) [abstract]

60.	S. Akbari (Joint with M. R. Oboudi) Cycles are determined by their domination polynomials Ars Combin. (Accepted) [abstract]

61.	S. Akbari, N. Ghareghani and G. B. Khosrovshahi (Joint with A. Mahmoody) On zero-sum 6-flows of graphs Linear Algebra Appl. 430 (2009), 3047-3052  [abstract]

62.	S. Akbari, D. Kiani and F. Ramezani Commuting graphs of group algebras Comm. Algebra (Accepted) [abstract]

63.	S. Akbari and E. Ghorbani (Joint with A. Mahmoodi) On graphs whose star sets are (co-)cliques Linear Algebra Appl. 430 (2009), 504-510  [abstract]

64.	S. Akbari and E. Ghorbani (Joint with M.R. Oboudi) Edge addition, singular values, and energy of graphs and matrices Linear Algebra Appl. 430 (2009), 2192-2199  [abstract]

65.	S. Akbari (Joint with M. Ghanbari and S. Jahanbekam) On the dynamic coloring of strongly regular graphs Ars Combin. (Accepted) [abstract]

66.	S. Akbari (Joint with F. Moazami and S. Zare) Kneser graphs and their complements are hyperenergetic MATCH Communications in Mathematical and in Computer Chemistry (Accepted) [abstract]

67.	S. Akbari (Joint with S.olouki, P. Hatami, and M. Siami) On signed edge domination number of graphs Discrete Math. (Accepted) [abstract]

68.	S. Akbari and E. Ghorbani Choice number and energy of graphs Linear Algebra Appl. 429 (2008), 2687-2690  [abstract]

69.	S. Akbari (Joint with H. Bidkhori and A. Mohammadian) Commuting graphs of matrix algebras Comm. Algebra (2008), 4020-4031  [abstract]

70.	S. Akbari and E. Ghorbani (Joint with S. Zare) Some relations between rank, chromatic number and energy of graphs Discrete Math. (Accepted) [abstract]

71.	S. Akbari and A. Mohammadian On zero-divisor graphs of finite rings J. Algebra 314 (2007), 168-184  [abstract]

72.	S. Akbari, A. Alipour and E. Ghorbani (Joint with J. Ebrahimi Boroojeni and M. Mirjalalieh Shirazi) Some relations between rank of a graph and its complement Linear Algebra Appl. 422 (2007), 341-347  [abstract]

73.	S. Akbari (Joint with A. Alipour) Multicolored trees in complete graphs J. Graph Theory 54 (2007), 221-232  [abstract]

74.	S. Akbari (Joint with A. Herman) Commuting decompositions of complete graphs J. Combin. Des. 15 (2007), 133-142  [abstract]

75.	S. Akbari and A. Alipour (Joint with H. L. Fu and Y. H. Lo) Multicolored parallelisms of isomorphic spanning trees SIAM J. Discrete Math. 20 (2006), 564-567  [abstract]

76.	S. Akbari and A. Mohammadian (Joint with H. Radjavi and P. Raja) On the diameters of commuting graphs Linear Algebra Appl. 418 (2006), 161-176  [abstract]

77.	S. Akbari and H. R. Maimani (Joint with A. Abdollahi) Non-commuting graph of a group J. Algebra 298 (2006), 468-492  [abstract]

78.	S. Akbari (Joint with V. S. Mirrokni and B. S. Sadjad) A relation between choosability and uniquely list colorability J. Combin. Theory Ser. B 96 (2006), 577-583  [abstract]

79.	S. Akbari, A. Alipour, E. Ghorbani and G. B. Khosrovshahi {−1,0,1}-basis for the null space of a forest Linear Algebra Appl. 414 (2006), 506-511  [abstract]

80.	S. Akbari, N. Ghareghani, G. B. Khosrovshahi and H. R. Maimani The kernels of the incidence matrices of graphs revisited Linear Algebra Appl. 414 (2006), 617-625  [abstract]

81.	S. Akbari, H. Bidkhori and N. Nosrati r-strong edge colorings of graphs Discrete Math. 306 (2006), 3005-3010  [abstract]

82.	S. Akbari and H. R. Fanai Some relations among term rank, clique number and list chromatic number of a graph Discrete Math. 306 (2006), 3078-3082  [abstract]

83.	S. Akbari and A. Mohammadian Zero-Divisor graphs of non-commutative rings J. Algebra 296 (2005), 462-479  [abstract]

84.	S. Akbari and H.R. Fanai Rank, term rank and chromatic number of a graph C. R. Acad. Sci. Paris. Ser. I 340 (2005), 181-184  [abstract]

85.	S. Akbari (Joint with A. Abdollahi) Rings virtually satisfying a polynomial identity J. Pure Appl. Algebra 198 (2005), 9-19  [abstract]

86.	S. Akbari and A. Mohammadian (Joint with M. Ghandehari and M. Hadian) On commuting graphs of semisimple rings Linear Algebra Appl. 390 (2004), 345-355  [abstract]

87.	S. Akbari and A. Alipour Transversals and multicolored matchings J. Combin. Des. 12 (2004), 325-332  [abstract]

88.	S. Akbari, H. R. Fanai and K. Mahmoudian On the matrices with constant determinant and permanent over roots of unity Linear Algebra Appl. 375 (2003), 245-249  [abstract]

89.	S. Akbari Two conjectures on uniquely totally colorable graphs Discrete Math. 266 (2003), 41-45  [abstract]

90.	S. Akbari, H. R. Maimani and S. Yassemi When a zero-divisor graph is planar or complete r-partite graph J. Algebra 270 (2003), 169-180  [abstract]

91.	S. Akbari, R. Ebrahimian, H. Momenaee Kermani and A. Salehi Golsefidy Maximal subgroups of GLn(D)* J. Algebra 259 (2003), 201-225  [abstract]

92.	S. Akbari and G. B. Khosrovshahi On the smallest edge defining sets of graphs Ars Combin. 63 (2002), 293-303  [abstract]

93.	H. Momenaee Kermani, S. Akbari, R. Ebrahimian and A. Salehi Golsefidy The group of units of an Artinian ring Algebra Colloq. 9 (2002), 81-88  [abstract]

94.	S. Akbari, H. R. Maimani and Ch. Maysoori Minimal defining sets for trivial 2-(v,3,v-2) designs Australas. J. Combin. 23 (2001), 5-8  [abstract]

95.	B. S. Sadjad, S. Akbari and V. S. Mirrokni Kr-free uniquely vertex colorable graphs with minimum possible edges J. Combin. Theory Ser. B 82 (2001), 316-318  [abstract]

96.	S. Akbari and M. Mahdavi-Hezavehi Normal subgroups of GLn(D) are not finitely generated Proc. Amer. Math. Soc. 128 (1999), 1627-1632  [abstract]

97.	S. Akbari, M. Mahdavi-Hezavehi and M. G. Mahmudi Maximal subgroups of GL1(D) J. Algebra 217 (1999), 422-433  [abstract]

98.	M. Mahdavi-Hezavehi and S. Akbari Some special subgroups of GLn(D) Algebra Colloq. 5 (1998), 361-370  [abstract]

99.	M. Arian-Nejad, S. Akbari and M. L. Mehrabadi On additive commutator groups in division rings Results Math. 33 (1998), 9-21  [abstract]

100.	S. Akbari, M. Behzad, H. Hajiabolhassan and E. S. Mahmoodian Uniquely total colorable graphs Graphs Combin. 13 (1997), 305-314  [abstract]

101.	S. Shahriari, S. Akbari, G. B. Khosrovshahi and Ch. Maysoori On maximum size anti-Pasch sets of triples London Math. Soc. Lecture Note Ser. (1997), 7-14  [abstract]