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, 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.

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.

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.

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

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.

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.

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.

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.