Distance-Regular Graphs of Diameter 3 Without Triangles with $c_2=2$

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.

Keywords

Distance-regular graph / Graph without triangles / Triple intersection numbers

References

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Funding

Российский Фонд Фундаментальных Исследований (РФФи)(20-51-53013)

National Natural Science Foundation of China(12171126)