Abstract
Earlier it was proved that some distance-regular graphs of diameter 3 with \(c_2=2\) do not exist. Distance-regular graph \(\varGamma \) with intersection array \(\{17,16,10;1,2,8\}\) has strongly regular graph \(\varGamma _{3}\) (pseudo-geometric graph for the net \(pG_9(17,9)\)). By symmetrizing the arrays of triple intersection numbers, it is proved that the distance-regular graphs with intersection arrays \(\{17,16,10;1,2,8\}\) and \(\{22,21,4;1,2,14\}\) do not exist.
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The study was supported by the RFBR and the NFSC (Project No. 20-51-53013), the second author is supported by the NNSF of China (No.12171126).
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Makhnev, A.A., Guo, W. & Efimov, K.S. Distance-Regular Graphs of Diameter 3 Without Triangles with \(c_2=2\). Commun. Math. Stat. 10, 785–792 (2022). https://doi.org/10.1007/s40304-021-00281-4
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DOI: https://doi.org/10.1007/s40304-021-00281-4