Browse issues
no. 1
Switching equivalence of strongly regular polar graphs
Nagy, Gábor P.1; Smaldore, Valentino2
1University of Szeged, Bolyai Institute, Aradi Vértanúk tere 1, H-6720 Szeged (Hungary), Budapest University of Technology and Economics, Institute of Mathematics, Műegyetem rkp. 3, H-1111 Budapest (Hungary)
2Università degli Studi di Padova, Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Stradella S. Nicola 3, 36100 Vicenza (Italy)
Algebraic Combinatorics, Volume 9 (2026) no. 1, pp. 289-305

We prove the switching equivalence of the strongly regular polar graphs $NO^\pm (4m,2)$, $NO^\mp (2m+1,4)$, and $\Gamma (O^\mp (4m,2))$ with an isolated vertex by giving an analytic description for them and their associated two-graphs.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.470
Classification: 05E30, 51A50
Keywords: strongly regular graphs, two-graphs, quadratic forms

Nagy, Gábor P.  1 ; Smaldore, Valentino  2

1 University of Szeged, Bolyai Institute, Aradi Vértanúk tere 1, H-6720 Szeged (Hungary), Budapest University of Technology and Economics, Institute of Mathematics, Műegyetem rkp. 3, H-1111 Budapest (Hungary)
2 Università degli Studi di Padova, Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Stradella S. Nicola 3, 36100 Vicenza (Italy)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{ALCO_2026__9_1_289_0,
     author = {Nagy, G\'abor P. and Smaldore, Valentino},
     title = {Switching equivalence of strongly regular polar graphs},
     journal = {Algebraic Combinatorics},
     pages = {289--305},
     year = {2026},
     publisher = {The Combinatorics Consortium},
     volume = {9},
     number = {1},
     doi = {10.5802/alco.470},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.470/}
}
TY  - JOUR
AU  - Nagy, Gábor P.
AU  - Smaldore, Valentino
TI  - Switching equivalence of strongly regular polar graphs
JO  - Algebraic Combinatorics
PY  - 2026
SP  - 289
EP  - 305
VL  - 9
IS  - 1
PB  - The Combinatorics Consortium
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.470/
DO  - 10.5802/alco.470
LA  - en
ID  - ALCO_2026__9_1_289_0
ER  - 
%0 Journal Article
%A Nagy, Gábor P.
%A Smaldore, Valentino
%T Switching equivalence of strongly regular polar graphs
%J Algebraic Combinatorics
%D 2026
%P 289-305
%V 9
%N 1
%I The Combinatorics Consortium
%U https://alco.centre-mersenne.org/articles/10.5802/alco.470/
%R 10.5802/alco.470
%G en
%F ALCO_2026__9_1_289_0
Nagy, Gábor P.; Smaldore, Valentino. Switching equivalence of strongly regular polar graphs. Algebraic Combinatorics, Volume 9 (2026) no. 1, pp. 289-305. doi: 10.5802/alco.470

[1] Bose, R. C. Strongly regular graphs, partial geometries and partially balanced designs, Pacific J. Math., Volume 13 (1963), pp. 389-419 | MR | DOI | Zbl

[2] Brouwer, A. E.; Haemers, W. H. Spectra of graphs, Universitext, Springer, New York, 2012, xiv+250 pages | DOI | MR | Zbl

[3] Brouwer, A. E.; van Lint, J. H. Strongly regular graphs and partial geometries, Enumeration and design (Waterloo, Ont., 1982), Academic Press, Toronto, ON, 1984, pp. 85-122 | MR | Zbl

[4] Brouwer, Andries E.; Van Maldeghem, H. Strongly regular graphs, Encyclopedia of Mathematics and its Applications, 182, Cambridge University Press, Cambridge, 2022, xvii+462 pages | DOI | MR | Zbl

[5] Bussemaker, F. C.; Mathon, R. A.; Seidel, J. J. Tables of two-graphs, Combinatorics and graph theory (Calcutta, 1980) (Lecture Notes in Math.), Volume 885, Springer, Berlin-New York, 1981, pp. 70-112 | MR | Zbl | DOI

[6] Grove, Larry C. Classical groups and geometric algebra, Graduate Studies in Mathematics, 39, American Mathematical Society, Providence, RI, 2002, x+169 pages | DOI | MR

[7] Hirschfeld, J. W. P. Projective geometries over finite fields, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979, xii+474 pages | MR | Zbl

[8] Hirschfeld, J. W. P.; Thas, J. A. General Galois geometries, Springer Monographs in Mathematics, Springer, London, 2016, xvi+409 pages | DOI | MR | Zbl

[9] Seidel, J. J. Graphs and two-graphs, Proceedings of the Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1974) (Congress. Numer.), Volume No. X, Utilitas Math., Winnipeg, MB (1974), pp. 125-143 | MR | Zbl

[10] Taylor, D. E. Regular 2-graphs, Proc. London Math. Soc. (3), Volume 35 (1977) no. 2, pp. 257-274 | DOI | MR | Zbl

Cited by Sources: