×

Computing distance-regular graph and association scheme parameters in SageMath with sage-drg. (English) Zbl 1436.05142

Summary: The sage-drg package for the SageMath computer algebra system has been originally developed for computation of parameters of distance-regular graphs. Recently, its functionality has been extended to handle general association schemes. The package has been used to obtain nonexistence results for both distance-regular graphs and \(Q\)-polynomial association schemes, mostly using the triple intersection numbers technique.

MSC:

05E30 Association schemes, strongly regular graphs
05C12 Distance in graphs
05-04 Software, source code, etc. for problems pertaining to combinatorics
PDFBibTeX XMLCite
Full Text: Link

References:

[1] E. Bannai and T. Ito.Algebraic Combinatorics I: Association Schemes. The Benjamin/Cummings Publishing Co., Inc., 1984. · Zbl 0555.05019
[2] A. E. Brouwer. “Parameters of distance-regular graphs”. 2011.Link.
[3] A. E. Brouwer. “Strongly regular graphs”. 2013.Link.
[4] A. E. Brouwer, A. M. Cohen, and A. Neumaier.Distance-regular graphs. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 18. Springer-Verlag, Berlin, 1989.Link. · Zbl 0747.05073
[5] K. Coolsaet and A. Juriši´c. “Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs”.J. Combin. Theory Ser. A115.6 (2008), pp. 1086-1095.Link. · Zbl 1182.05132
[6] E. van Dam, W. Martin, and M. Muzychuk. “Uniformity in association schemes and coherent configurations: cometricQ-antipodal schemes and linked systems”.J. Combin. Theory Ser. A120.7 (2013), pp. 1401-1439.Link. · Zbl 1314.05236
[7] E. R. van Dam, J. H. Koolen, and H. Tanaka. “Distance-regular graphs”.Electron. J. Combin. DS(2016), p. 22.Link. · Zbl 1335.05062
[8] P. Delsarte.An algebraic approach to the association schemes of coding theory. Philips Res. Rep. Suppl. 10. Historical Jrl., Ann Arbor, MI, 1973. · Zbl 1075.05606
[9] J. Forrest et al.coin-or/Cbc: COIN-OR Branch-and-Cut MIP Solver, version 2.9.4. 2015.Link. Link.
[10] A. Gavrilyuk, S. Suda, and J. Vidali. “On tight 4-designs in Hamming association schemes”. 2018.arXiv:1809.07553.
[11] B. G. Kodalen. “Linked systems of symmetric designs”.Algebr. Comb.2.1 (2019), pp. 119- 147.Link. · Zbl 1405.05195
[12] A. Makhorin.GLPK (GNU Linear Programming Kit) v4.63.p2. 2012.Link.
[13] W. J. Martin, M. Muzychuk, and J. Williford. “Imprimitive cometric association schemes: constructions and analysis”.J. Algebraic Combin.25.4 (2007), pp. 399-415.Link. · Zbl 1118.05100
[14] W. J. Martin and H. Tanaka. “Commutative association schemes”.European J. Combin.30.6 (2009), pp. 1497-1525.Link. · Zbl 1228.05317
[15] Maxima.Maxima, a Computer Algebra System. Version 5.39.0. 2017.Link.
[16] G. E. Moorhouse and J. Williford. “Double covers of symplectic dual polar graphs”.Discrete Math.339.2 (2016), pp. 571-588.Link. · Zbl 1327.05344
[17] T. Penttila and J. Williford. “New families ofQ-polynomial association schemes”.J. Combin. Theory Ser. A118.2 (2011), pp. 502-509.Link. · Zbl 1257.05183
[18] Python Software Foundation.Python Language Reference, version 2.7.13. 2017.Link.
[19] The Sage Developers.SageMath, the Sage Mathematics Software System (Version 7.6). 2017. Link.
[20] J. Vidali. “Description of thesage-drgpackage”.Electron. J. Combin.25.4 (2018), P4.21 (appendix).Link.
[21] J. Vidali.jaanos/sage-drg:sage-drgSage package v0.8. 2018.Link.Link.
[22] J. Vidali. “Using symbolic computation to prove nonexistence of distance-regular graphs”. Electron. J. Combin.25.4 (2018), P4.21.Link. · Zbl 1401.05320
[23] J.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.