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Volumn 10, Issue 1 R, 2003, Pages

Switching of edges in strongly regular graphs. I. A family of partial difference sets on 100 vertices

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EID: 3042578220     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: 10.37236/1710     Document Type: Article
Times cited : (31)

References (55)
  • 2
    • 0000895903 scopus 로고
    • Isomorphism problem for a class of point-symmetric structures
    • [Bab77] L. Bábái, Isomorphism problem for a class of point-symmetric structures, Acta Math. Acad. Sci. Hung. 29, 329-336, 1977.
    • (1977) Acta Math. Acad. Sci. Hung. , vol.29 , pp. 329-336
    • Bábái, L.1
  • 3
    • 3042555369 scopus 로고
    • A new strongly regular graph admitting the Hall-Janko-Wales group
    • Stat.-Math. Division, Indian Statistical Institute, Calcutta, Sept.23
    • [Bag88] B. Bagchi, A new strongly regular graph admitting the Hall-Janko-Wales group. Tech. Report No. 13/88. Stat.-Math. Division, Indian Statistical Institute, Calcutta, Sept.23, 1988.
    • (1988) Tech. Report No. 13/88
    • Bagchi, B.1
  • 4
    • 3042602221 scopus 로고
    • A regular two-graph admitting the Hall-Janko-Wales group
    • [Bag92] B. Bagchi, A regular two-graph admitting the Hall-Janko-Wales group. Sankhya, Ser. A, Spec. Volume 54, 35-45, 1992.
    • (1992) Sankhya, Ser. A , vol.54 SPEC. VOLUME , pp. 35-45
    • Bagchi, B.1
  • 6
    • 3042595578 scopus 로고
    • Seidel-equivalence of strongly regular graphs
    • [BhaS68] Bhagwandas and S. S. Shrikhande, Seidel-equivalence of strongly regular graphs, Sankhya, Ser. A 30, 359-368, 1968.
    • (1968) Sankhya, Ser. A , vol.30 , pp. 359-368
    • Bhagwandas1    Shrikhande, S.S.2
  • 7
    • 0000675946 scopus 로고
    • Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture
    • [BosPS60] R. C. Bose, E. T. Parker and S. S. Shrikhande, Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture, Canad. J. Math. 12, 189-203, 1960.
    • (1960) Canad. J. Math. , vol.12 , pp. 189-203
    • Bose, R.C.1    Parker, E.T.2    Shrikhande, S.S.3
  • 9
    • 0009030635 scopus 로고    scopus 로고
    • Strongly regular graphs
    • eds.: Colbourn and Dinitz, CRC Press
    • [ Bro96] A. E. Brouwer, Strongly regular graphs, in: The CRC Handbook of Combinatorial Designs (eds.: Colbourn and Dinitz), 667-685, CRC Press, 1996.
    • (1996) The CRC Handbook of Combinatorial Designs , pp. 667-685
    • Brouwer, A.E.1
  • 13
    • 0346156127 scopus 로고    scopus 로고
    • Three-class association schemes
    • [Dam99] E. R. van Dam, Three-class association schemes, J. Algebraic Combin. 10, 69-107, 1999.
    • (1999) J. Algebraic Combin. , vol.10 , pp. 69-107
    • Van Dam, E.R.1
  • 15
    • 0002409906 scopus 로고
    • Cellular rings and groups of automorphisms of graphs
    • (eds.: Faradžev, Ivanov, Klin and Woldar), Kluwer Academic Publishers
    • [FarKM94] I. A. Faradžev, M. H. Klin and M. E. Muzichuk, Cellular rings and groups of automorphisms of graphs, in: Investigations in algebraic theory of combinatorial objects (eds.: Faradžev, Ivanov, Klin and Woldar), Kluwer Academic Publishers, 1994, pp. 1-152.
    • (1994) Investigations in Algebraic Theory of Combinatorial Objects , pp. 1-152
    • Faradžev, I.A.1    Klin, M.H.2    Muzichuk, M.E.3
  • 16
    • 0009363208 scopus 로고
    • Maximal subgroups of the Hall-Janko-Wales group
    • [FinR73] L. Finkelstein and A. Rudvalis, Maximal subgroups of the Hall-Janko-Wales group, J. Algebra 24, 486-493, 1973.
    • (1973) J. Algebra , vol.24 , pp. 486-493
    • Finkelstein, L.1    Rudvalis, A.2
  • 19
    • 0141484143 scopus 로고
    • Graphs with maximal even girth
    • [Gew69] A. Gewirtz, Graphs with maximal even girth, Canad. J. Math. 21, 915-934, 1969.
    • (1969) Canad. J. Math. , vol.21 , pp. 915-934
    • Gewirtz, A.1
  • 20
    • 0043278321 scopus 로고
    • Constructing cospectral graphs
    • [GodM82] C. D. Godsil and B. D. McKay, Constructing cospectral graphs, Aequationes Math. 25, 257-268, 1982.
    • (1982) Aequationes Math. , vol.25 , pp. 257-268
    • Godsil, C.D.1    McKay, B.D.2
  • 21
    • 0041011039 scopus 로고
    • Strongly regular graphs derived from combinatorial designs
    • [GoeS70] J.-M. Goethals and J.J. Seidel, Strongly regular graphs derived from combinatorial designs, Canad. J. Math. 22, 597-614, 1970.
    • (1970) Canad. J. Math. , vol.22 , pp. 597-614
    • Goethals, J.-M.1    Seidel, J.J.2
  • 22
    • 0242635844 scopus 로고    scopus 로고
    • New difference sets in nonabelian groups of order 100
    • [GolV01] A. Golemac and T. Vučičić, New difference sets in nonabelian groups of order 100, J. Combin. Designs 9, 424-434, 2001.
    • (2001) J. Combin. Designs , vol.9 , pp. 424-434
    • Golemac, A.1    Vučičić, T.2
  • 23
    • 31244432138 scopus 로고    scopus 로고
    • New (100,45,20) symmetric designs and Bush-type Hadamard matrices of order 100
    • [GolV02] A. Golemac and T. Vučičić, New (100,45,20) symmetric designs and Bush-type Hadamard matrices of order 100, Discr. Math. 245, 263-272, 2002.
    • (2002) Discr. Math. , vol.245 , pp. 263-272
    • Golemac, A.1    Vučičić, T.2
  • 24
    • 0038992785 scopus 로고
    • Strongly regular graphs with strongly regular decompositions
    • [HaeH89] W. H. Haemers and D. G. Higman, Strongly regular graphs with strongly regular decompositions, Linear Algebra Appl. 114(115), 379-398, 1989.
    • (1989) Linear Algebra Appl. , vol.114 , Issue.115 , pp. 379-398
    • Haemers, W.H.1    Higman, D.G.2
  • 25
    • 0000231398 scopus 로고
    • Cyclic projective planes
    • [Hal47] M. Hall, Cyclic projective planes, Duke Math. J. 14, 1079-1090, 1947.
    • (1947) Duke Math. J. , vol.14 , pp. 1079-1090
    • Hall, M.1
  • 26
    • 0011664913 scopus 로고
    • The simple group of order 604,800
    • [HalW68] M. Hall, Jr. and D. Wales, The simple group of order 604,800, J. Algebra 9 417-450, 1968.
    • (1968) J. Algebra , vol.9 , pp. 417-450
    • Hall Jr., M.1    Wales, D.2
  • 29
    • 0039486218 scopus 로고
    • Rank 3 groups and strongly regular graphs
    • [HesH71] M. D. Hestenes and D. G. Higman, Rank 3 groups and strongly regular graphs, SIAM-AMS Proceedings 4, 141-159, 1971.
    • (1971) SIAM-AMS Proceedings , vol.4 , pp. 141-159
    • Hestenes, M.D.1    Higman, D.G.2
  • 30
    • 0000127539 scopus 로고
    • A simple group of order 44,352,000
    • [HigS68] D. G. Higman and C. C. Sims, A simple group of order 44,352,000, Math. Zeitschrift 105 110-113, 1968.
    • (1968) Math. Zeitschrift , vol.105 , pp. 110-113
    • Higman, D.G.1    Sims, C.C.2
  • 34
    • 0002842650 scopus 로고
    • Some new simple groups of finite order. I
    • INDAM, Rome, 1967/68, Academic Press
    • [Jan69] Z. Janko, Some new simple groups of finite order. I, Symposia Mathematica (INDAM, Rome, 1967/68), 1, 25-64, Academic Press, 1969.
    • (1969) Symposia Mathematica , vol.1 , pp. 25-64
    • Janko, Z.1
  • 35
    • 0013525507 scopus 로고    scopus 로고
    • Bush-type Hadamard matrices and symmetric designs
    • [JanKT01] Z. Janko, H. Kharaghani and V. D. Tonchev, Bush-type Hadamard matrices and symmetric designs, J. Combin. Designs 9, 72-78, 2001.
    • (2001) J. Combin. Designs , vol.9 , pp. 72-78
    • Janko, Z.1    Kharaghani, H.2    Tonchev, V.D.3
  • 36
    • 3042684412 scopus 로고    scopus 로고
    • Partial difference sets for known and new strongly regular graphs
    • September 3-14, 2000, Varna, Bulgaria. Inst. of Math. and Inform., Bulgarian Academy of Sciences. Sofia
    • [Kli00] M. Klin, Partial difference sets for known and new strongly regular graphs. In: Summer School ALCCAL 2000. Algebraic Combinatorics and Computer Algebra. September 3-14, 2000, Varna, Bulgaria. Inst. of Math. and Inform., Bulgarian Academy of Sciences. Sofia 2000, pp. 59-60.
    • (2000) Summer School ALCCAL 2000. Algebraic Combinatorics and Computer Algebra , pp. 59-60
    • Klin, M.1
  • 39
    • 3042646364 scopus 로고    scopus 로고
    • Constructive representation theoretic methods and non-abelian difference sets
    • (eds: Pott, Kumar, Helleseth, Jungnickel), Kluwer Academic Publishers
    • [Lie99] R.A.Liebler. Constructive representation theoretic methods and non-abelian difference sets, in: Difference sets, sequences and their correlation properties (eds: Pott, Kumar, Helleseth, Jungnickel), Kluwer Academic Publishers, 1999, pp. 331-352.
    • (1999) Diffrence Sets, Sequences and Their Correlation Properties , pp. 331-352
    • Liebler, R.A.1
  • 40
    • 0011406814 scopus 로고
    • Equilateral point sets in elliptic geometry
    • [vLinS66] J. H. van Lint and J. J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math. 28, 335-348, 1966.
    • (1966) Indag. Math. , vol.28 , pp. 335-348
    • Van Lint, J.H.1    Seidel, J.J.2
  • 41
    • 85088006343 scopus 로고
    • 5(10) association scheme
    • 5(10) association scheme, Chin. Ann. of Math. 48, 355-356, 1983.
    • (1983) Chin. Ann. of Math. , vol.48 , pp. 355-356
    • Zhangwen, L.1
  • 42
    • 37949014986 scopus 로고
    • Partial difference sets
    • [Ma84] S. L. Ma, Partial difference sets, Discrete Math. 52, 75-89, 1984.
    • (1984) Discrete Math. , vol.52 , pp. 75-89
    • Ma, S.L.1
  • 43
    • 0042505974 scopus 로고
    • A survey of partial difference sets
    • [Ma94] S. L. Ma, A survey of partial difference sets, Des. Codes Cryptogr. 4, 221-261, 1994.
    • (1994) Des. Codes Cryptogr. , vol.4 , pp. 221-261
    • Ma, S.L.1
  • 44
    • 84966256366 scopus 로고
    • The subgroup structure of the Higman-Sims simple group
    • [Mag71] S. S. Magliveras, The subgroup structure of the Higman-Sims simple group, Bull. Amer. Math. Soc. 77, 535-539, 1971.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 535-539
    • Magliveras, S.S.1
  • 45
    • 0004010079 scopus 로고
    • Technical report TR-CS-90-02, Australian National University, Computer Science Department, ANU
    • [McKay90] B.D. McKay, nauty user's guide (version 1.5), Technical report TR-CS-90-02, Australian National University, Computer Science Department, ANU, 1990.
    • (1990) Nauty User's Guide (Version 1.5)
    • McKay, B.D.1
  • 46
    • 0042284276 scopus 로고    scopus 로고
    • On graphs with three eigenvalues
    • [MuzK98] M. Muzychuk and M. Klin, On graphs with three eigenvalues, Discrete Math. 189, 191-207, 1998.
    • (1998) Discrete Math. , vol.189 , pp. 191-207
    • Muzychuk, M.1    Klin, M.2
  • 47
    • 3042688585 scopus 로고
    • Classification of (16,6,2)-designs by ovals
    • [Rog84] N. N. Roghelia and S. S. Sane, Classification of (16,6,2)-designs by ovals, Discrete Math. 51, 161-177, 1984.
    • (1984) Discrete Math. , vol.51 , pp. 161-177
    • Roghelia, N.N.1    Sane, S.S.2
  • 48
    • 3042591458 scopus 로고
    • (v, k, λ)-graphs and polarities of (v, k, λ)-designs
    • [Rud71] A. Rudvalis, (v, k, λ)-graphs and polarities of (v, k, λ)-designs, Math. Zeitschr. 120, 224-230, 1971.
    • (1971) Math. Zeitschr. , vol.120 , pp. 224-230
    • Rudvalis, A.1
  • 49
    • 0040671555 scopus 로고
    • 2-type and of triangular type
    • 2-type and of triangular type, Indag. Math. 29, 188-196, 1967.
    • (1967) Indag. Math. , vol.29 , pp. 188-196
    • Seidel, J.J.1
  • 50
    • 0038236794 scopus 로고
    • GRAPE: A system for computing with graphs and groups
    • Groups and Computation (eds.: Finkelstein and Kantor), American Mathematical Society
    • [Soi93] L. H. Soicher. GRAPE: a system for computing with graphs and groups. In: Groups and Computation (eds.: Finkelstein and Kantor), volume 11 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 287-291. American Mathematical Society, 1993.
    • (1993) DIMACS Series in Discrete Mathematics and Theoretical Computer Science , vol.11 , pp. 287-291
    • Soicher, L.H.1
  • 51
    • 0003071185 scopus 로고
    • Non-abelian Hadamard difference sets
    • [Smi95] K. W. Smith, Non-abelian Hadamard difference sets, J. Combin. Theory Ser. A 70, 144-156, 1995.
    • (1995) J. Combin. Theory Ser. A , vol.70 , pp. 144-156
    • Smith, K.W.1
  • 52
    • 84972540358 scopus 로고
    • Character sums and difference sets
    • [Tur65] R. J. Turyn, Character sums and difference sets, Pacific J. Math. 15, 319-346, 1965.
    • (1965) Pacific J. Math. , vol.15 , pp. 319-346
    • Turyn, R.J.1
  • 53
    • 3042602220 scopus 로고    scopus 로고
    • New symmetric designs and nonabelian difference sets with parameters (100,45,20)
    • [Vǔc00] T. Vučičić, New symmetric designs and nonabelian difference sets with parameters (100,45,20), J. Combin. Designs 8, 291-299, 2000.
    • (2000) J. Combin. Designs , vol.8 , pp. 291-299
    • Vučičić, T.1
  • 54
    • 84972498296 scopus 로고
    • Uniqueness of the graph of a rank three group
    • [Wal69] D. Wales, Uniqueness of the graph of a rank three group, Pacific J. Math. 30, 271-276, 1969.
    • (1969) Pacific J. Math. , vol.30 , pp. 271-276
    • Wales, D.1
  • 55
    • 0001131103 scopus 로고
    • Maximal subgroups of automorphism groups of simple groups
    • [Wil85] R. A. Wilson, Maximal subgroups of automorphism groups of simple groups, J. London Math. Soc. (2) 32, 460-466, 1985.
    • (1985) J. London Math. Soc. (2) , vol.32 , pp. 460-466
    • Wilson, R.A.1


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