sage-drg swMATH ID: 26413 Software Authors: Vidali, Janoš Description: Using symbolic computation to prove nonexistence of distance-regular graphs. A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular 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/sage-drg Source Code: https://github.com/jaanos/sage-drg Dependencies: Sage Keywords: distance-regular graphs; Krein parameters; triple intersection numbers; nonexistence; symbolic computation Related Software: SageMath; GLPK; Maxima; Python; Magma; Cbc; Mathematica Cited in: 5 Documents Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Computing distance-regular graph and association scheme parameters in SageMath with sage-drg. Zbl 1436.05142Vidali, Janoš 2019 Using symbolic computation to prove nonexistence of distance-regular graphs. Zbl 1401.05320Vidali, Janoš 2018 Cited by 5 Authors 3 Vidali, Janoš 2 Gavrilyuk, Alexander L. 1 Herman, Allen 1 Koolen, Jack H. 1 Williford, Jason S. Cited 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 Cited in 4 Fields 5 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) Citations by Year