sagedrg
swMATH ID:  26413 
Software Authors:  Vidali, Janoš 
Description:  Using symbolic computation to prove nonexistence of distanceregular graphs. A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distanceregular graph. We use this tool to show that there is no distanceregular graph with intersection array {(2r+1)(4r+1)(4t−1),8r(4rt−r+2t),(r+t)(4r+1);1,(r+t)(4r+1),4r(2r+1)(4t−1)} (r,t≥1), {135,128,16;1,16,120}, {234,165,12;1,30,198} or {55,54,50,35,10;1,5,20,45,55}. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. Further combinatorial arguments are then used to derive nonexistence. 
Homepage:  https://github.com/jaanos/sagedrg 
Dependencies:  Sage 
Keywords:  distanceregular graphs; Krein parameters; triple intersection numbers; nonexistence; symbolic computation 
Related Software:  SageMath; GLPK; Python; Maxima; Magma; Cbc; Mathematica 
Referenced in:  5 Publications 
Standard Articles
2 Publications describing the Software, including 2 Publications in zbMATH  Year 

Computing distanceregular graph and association scheme parameters in SageMath with sagedrg. Zbl 1436.05142 Vidali, Janoš 
2019

Using symbolic computation to prove nonexistence of distanceregular graphs. Zbl 1401.05320 Vidali, Janoš 
2018

Referenced by 5 Authors
3  Vidali, Janoš 
2  Gavrilyuk, Alexander L. 
1  Herman, Allen 
1  Koolen, Jack H. 
1  Williford, Jason S. 
Referenced in 5 Serials
1  Indian Journal of Pure & Applied Mathematics 
1  The Electronic Journal of Combinatorics 
1  Séminaire Lotharingien de Combinatoire 
1  Ars Mathematica Contemporanea 
1  Arabian Journal of Mathematics 
Referenced in 4 Fields
5  Combinatorics (05XX) 
1  Number theory (11XX) 
1  Associative rings and algebras (16XX) 
1  Group theory and generalizations (20XX) 