Parameters of Strongly Regular Graphs - References

Jernej Azarija & Tilen Marc,
There is no (75,32,10,16) strongly regular graph, arXiv:1509.05933, Dec. 2015.

Jernej Azarija & Tilen Marc,
There is no (95,40,12,20) strongly regular graph, arXiv:1603.02032, Mar. 2016.

Majid Behbahani & Clement Lam,
Strongly regular graphs with non-trivial automorphisms, Discr. Math. 311 (2011) 132-144.

Andriy V. Bondarenko & Danylo V. Radchenko,
On a family of strongly regular graphs with λ = 1, arXiv:1201.0383, Feb. 2012.

A. V. Bondarenko, A. Prymak & D. Radchenko,
Non-existence of (76,30,8,14) strongly regular graph and some structural tools,
arXiv:1410.6748, Oct. 2014.

A. V. Bondarenko, A. Mellit, A. Prymak, D. Radchenko & M. Viazovska,
There is no strongly regular graph with parameters (460,153,32,60),
arXiv:1509.06286, Sep. 2015.

Iliya Bouyukliev, Veerle Fack, Wolfgang Willems & Joost Winne,
Projective two-weight codes with small parameters and their corresponding graphs,
Designs Codes Cryptogr. 41 (2006) 59-78.

A. E. Brouwer,
The uniqueness of the strongly regular graph on 77 points,
J. Graph Th. 7 (1983) 455-461.

A. E. Brouwer,
Some new two-weight codes and strongly regular graphs,
Discrete Applied Math. 10 (1985) 111-114.

A. E. Brouwer & W. H. Haemers,
Structure and uniqueness of the (81,20,1,6) strongly regular graph,
Discrete Math. 106/107 (1992) 77-82.

A. E. Brouwer, J. H. Koolen & M. H. Klin,
A root graph that is locally the line graph of the Petersen graph,
Discr. Math. 264 (2003) 13-24.

A. E. Brouwer & A. Neumaier,
A remark on partial linear spaces of girth 5 with an application to strongly regular graphs,
Combinatorica 8 (1988) 57-61.

F. C. Bussemaker, W. H. Haemers, R. Mathon & H. A. Wilbrink,
A (49,16,3,6) strongly regular graph does not exist,
European J. Combin. 10 (1989) 413-418.

P. J. Cameron, J.-M. Goethals & J. J. Seidel,
Strongly regular graphs having strongly regular subconstituents,
J. Algebra 55 (1978) 257-280.

L. C. Chang,
Association schemes of partially balanced block designs with parameters v = 28, n1 = 12, n2 = 15 and p112 = 4,
Sci. Record 4 (1960) 12-18.

Arjeh M. Cohen,
A new partial geometry with parameters (s,t,α) = (7,8,4),
J. Geometry 16 (1981) 181-186.

K. Coolsaet,
The uniqueness of the strongly regular graph srg(105,32,4,12),
Simon Stevin 12 (2005) 707-718.

K. Coolsaet, J. Degraer & E. Spence,
The Strongly Regular (45,12,3,3) graphs,
Electr. J. Combin. 13 (2006) R32.

K. Coolsaet & J. Degraer,
Using algebraic properties of minimal idempotents for exhaustive computer generation of association schemes,
Electr. J. Combin. 15 (2008) R30.

Antonio Cossidente & Tim Penttila,
Hemisystems on the Hermitian surface,
J. London Math. Soc. 72 (2005) 731-741.

Dean Crnković & Marija Maksimović,
Construction of strongly regular graphs having an automorphism group of composite order,
Contrib. Discrete Math. 15 (2020) 22-41.

Dean Crnković & Marija Maksimović,
Strongly regular graphs with parameters (37, 18, 8, 9) having nontrivial automorphisms,
The Art of Discrete and Applied Mathematics 3 (2020) #P2.10.

Dean Crnković, Sanja Rukavina & Andrea Švob,
Strongly regular graphs from orthogonal groups O+(6,2) and O(6,2),
arXiv:1609.07133, Sep. 2016.

Frank De Clerck & Mario Delanote,
Partial geometries and the triality quadric,
J. Geometry 68 (2000) 34-47.

Frank De Clerck, Mario Delanote, Nicholas Hamilton & Rudolf Mathon,
Perp-systems and partial geometries,
Adv. Geom. 2 (2002) 1-12.

J. Degraer,
Isomorph-free exhaustive generation algorithms for association schemes,
PhD Thesis, Ghent University, 2007.

J. Degraer & K. Coolsaet,
Classification of some strongly regular subgraphs of the McLaughlin graph,
Discr. Math. 308 (2008) 395-400.

Luis A. Dissett,
Combinatorial and computational aspects of finite geometries,
Ph.D. Thesis, Toronto, 2000.

Suzanne Dixmier & François Zara,
Essai d'une méthode d'étude de certains graphes liés aux groupes classiques,
C. R. Acad. Sc. Paris (A) 282 (1976) 259-262.

Matthew Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson & Cody E. Watson,
Equiangular tight frames with centroidal symmetry,
arXiv:1509.04059, Sep. 2015.

Matthew Fickus, John Jasper, Dustin G. Mixon & Jesse Peterson,
Tremain equiangular tight frames,
arXiv:1602.03490, Feb. 2016.

F. Fiedler & M. Klin,
A strongly regular graph with the parameters (512,73,438,12,10) and its dual graph,
Preprint MATH-AL-7-1998, Technische Universität Dresden, July 1998, 23 pp.

A. L. Gavrilyuk & A. A. Makhnev,
On Krein Graphs without Triangles,
Dokl. Akad. Nauk 403 (2005) 727-730 (Russian) / Doklady Mathematics 72 (2005) 591-594 (English).

A. Gewirtz,
Graphs with maximal even girth,
Canad. J. Math. 21 (1969) 915-934.

A. Gewirtz,
The uniqueness of g(2,2,10,56),
Trans. New York Acad. Sci. 31 (1969) 656-675.

C. D. Godsil,
Krein covers of complete graphs,
Australasian J. Comb. 6 (1992) 245-255.

J.-M. Goethals & J. J. Seidel,
Strongly regular graphs derived from combinatorial designs,
Can. J. Math. 22 (1970) 597-614.

J.-M. Goethals & J. J. Seidel,
The regular two-graph on 276 vertices,
Discr. Math. 12 (1975) 143-158.

Anka Golemac, Joško Mandić & Tanja Vučičić,
New regular partial difference sets and strongly regular graphs with parameters (96,20,4,4) and (96,19,2,4),
Electr. J. Combin. 13 (2006) R88.

Oleg Gritsenko,
On strongly regular graph with parameters (65, 32, 15, 16), arXiv:2102.05432, Feb 2021.

T. Aaron Gulliver,
Two new optimal ternary two-weight codes and strongly regular graphs,
Discr. Math. 149 (1996) 83-92.

T. A. Gulliver,
A new two-weight code and strongly regular graph,
Appl. Math. Letters 9 (1996) 17-20.

W. H. Haemers,
A new partial geometry constructed from the Hoffman-Singleton graph,
pp. 119-127 in: Finite Geometries and designs, Proc. Second Isle of Thorns Conference 1980, P.J. Cameron, J.W.P. Hirschfeld & D.R. Hughes (eds.), London Math. Soc. Lecture Note Ser. 49, Cambridge University Press, Cambridge, 1981.

W. Haemers,
There exists no (76,21,2,7) strongly regular graph,
pp. 175-176 in: Finite Geometry and Combinatorics, F. De Clerck et al. (eds.), LMS Lecture Notes Series 191, Cambridge University Press, 1993.

W. Haemers & E. Spence,
The Pseudo-Geometric Graphs for Generalised Quadrangles of Order (3,t),
Europ. J. Comb. 22 (2001) 839-845.

D. G. Higman & C. Sims,
A simple group of order 44,352,000,
Math.Z. 105 (1968) 110-113.

Raymond Hill,
On the largest size of cap in S5,3,
Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat. (8) 54 (1973) 378-384.

Raymond Hill,
Caps and groups,
pp. 389-394 in: Proc. Rome 1973, Atti dei Convegni Lincei, 1976.

A. J. Hoffman & R. R. Singleton,
On Moore graphs with diameters 2 and 3,
IBM J. Res. Develop. 4 (1960) 497-504.

Tayuan Huang, Lingling Huang & Miaow-Ing Lin,
On a class of strongly regular designs and quasi-semisymmetric designs,
pp. 129-153 in: Recent developments in algebra and related areas, Chongying Dong et al. eds. Papers of the international conference on algebra and related areas, Tsinghua University, Beijing, China, August 18-20, 2007. Dedicated to Zhexian Wan in honor of his 80th birthday. Advanced Lectures in Mathematics (ALM) 8 (2009) 129-153.

Yury Ionin & Hadi Kharaghani,
New Families of Strongly Regular Graphs,
J. of Combin. Designs 11 (2003) 208-217.

Zvonimir Janko & Hadi Kharaghani,
A Block Negacyclic Bush-Type Hadamard Matrix and Two Strongly Regular Graphs,
J. Combinatorial Th. (A) 98 (2002) 118-126.

L. K. Jørgensen & M. H. Klin,
Switching of edges in strongly regular graphs. I.: A family of partial difference sets on 100 vertices,
Electr. J. Combin. 10 (2003) R17.

Petteri Kaski & Patric R. J. Östergård,
There are exactly five biplanes with k = 11,
J. Combinatorial Designs 16 (2007) 117-127.

Mikhail Klin, Christian Pech, Sven Reichard, Andrew Woldar & Matan Ziv-Av,
Examples of computer experimentation in algebraic combinatorics,
Ars Math. Contemp. 3 (2010) 237-258.

Axel Kohnert,
Constructing two-weight codes with prescribed groups of automorphisms,
Discr. Appl. Math. 155 (2007) 1451-1457.

C. W. H. Lam, L. Thiel, S. Swiercz & J. McKay,
The nonexistence of ovals in a projective plane of order 10, Discr. Math. 45 (1983) 319-321.

C. L. M. de Lange,
Some New Cyclotomic Strongly Regular Graphs,
J. Algebraic Combin. 4 (1995) 329-330.

J. H. van Lint & A. Schrijver,
Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields,
Combinatorica 1 (1981) 63-73.

A. A. Makhnev,
On the Nonexistence of Strongly Regular Graphs with Parameters (486, 165, 36, 66),
Ukrainian Math. J. 54 (2002) 1137-1146.

A. A. Makhnev,
The graph Kre(4) does not exist,
Doklady Math. 96 (2017) 348-350.

R. A. Mathon,
Symmetric conference matrices of order pq2 + 1,
Canad. J. Math. 30 (1978) 321-331.

B. D. McKay & E. Spence,
Classification of regular two-graphs on 36 and 38 vertices,
Australasian J. of Combin. 24 (2001) 293-300.

Dale M. Mesner,
Negative Latin square designs,
Institute of Statistics, UNC, NC Mimeo series 410, November 1964.

Mikhail Muzychuk,
A generalization of Wallis-Fon-Der-Flaass construction of strongly regular graphs,
J. Algebr. Comb. 25 (2007) 169-187.

Patric R. J. Östergård & Leonard H. Soicher,
There is No McLaughlin Geometry,
arXiv:1607.03372, Jul 2016.

Dmitrii V. Pasechnik,
Skew-symmetric association schemes with two classes and strongly regular graphs of type L2n-1(4n-1),
Acta Applicandae Mathematicae 29 (1992) 129-138.

A. J. L. Paulus,
Conference matrices and graphs of order 26,
Technische Hogeschool Eindhoven, report WSK 73/06, Eindhoven, 1973, 89 pp.

T. Penttila & G. F. Royle,
Sets of type (m,n) in the affine and projective planes of order nine,
Designs Codes Cryptogr. 6 (1995) 229-245.

J. Petersen,
Sur le théorème de Tait,
L'Intermédiaire des Mathématiciens 5 (1898) 225-227.

John Polhill,
Generalizations of partial difference sets from cyclotomy to nonelementary abelian p-groups,
Electr. J. Combin. 15 (2008) R125.

John Polhill,
Negative Latin Square type partial difference sets and amorphic association schemes with Galois rings,
J. Combinatorial Designs 17 (2009) 266-282.

M. J. de Resmini,
A 35-set of type (2,5) in PG(2,9),
J. Combin. Th. (A) 45 (1987) 303-305.

M. J. de Resmini & Grazia Migliori,
A 78-set of Type (2,6) in PG(2,16),
Ars Combin. 22 (1986) 73-75.

М. З. Розенфельд = M. Z. Rozenfel'd,
О построении и свойствах некоторых классов сильно регулярных графов = The construction and properties of certain classes of strongly regular graphs (Russian), Uspehi Mat. Nauk 28 (1973), no. 3 (171), 197-198.
[ Explicit matrices are given in Weisfeiler, Chapters U and V. ]

J. J. Seidel,
Strongly regular graphs with (-1,1,0) adjacency matrix having eigenvalue 3,
Lin. Alg. Appl. 1 (1968) 281-298.

S. S. Shrikhande,
The uniqueness of the L2 association scheme,
Ann. Math. Statist. 30 (1959) 781-798.

E. Spence,
The Strongly Regular (40,12,2,4) Graphs,
Electr. J. Combin. 7 (2000) R22.

G. Tarry,
Le problème des 36 officiers, Comptes rendus de l'association française pour l'avancement des sciences, Paris 29 (1901) 170-203.

W. D. Wallis,
Construction of strongly regular graphs using affine designs,
Bull. Austral. Math. Soc. 4 (1971) 41-49. Corrigenda, ibid. 5 (1971) 431.

Boris Weisfeiler,
On Construction and Identification of Graphs, Springer LNM 558, 1976.

H. A. Wilbrink & A. E. Brouwer,
A (57,14,1) strongly regular graph does not exist,
Indag. Math. 45 (1983) 117-121.