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
Dependencies: Sage
Keywords: distance-regular graphs; Krein parameters; triple intersection numbers; nonexistence; symbolic computation
Related Software: SageMath; GLPK; Python; Maxima; Magma; Cbc; Mathematica
Referenced in: 5 Publications

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