Abstract
We prove that the arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} cannot be realized as the intersection arrays of distance-regular graphs. In the proof we use some inequalities bounding the size of substructures (cliques, cocliques) in a distance-regular graph.
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This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Geometric and Algebraic Combinatorics”.
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Gavrilyuk, A.L., Makhnev, A.A. Distance-regular graphs with intersection arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} do not exist. Des. Codes Cryptogr. 65, 49–54 (2012). https://doi.org/10.1007/s10623-012-9695-1
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DOI: https://doi.org/10.1007/s10623-012-9695-1