arXiv subjects
Publications and source records attributed to Alexander Gavrilyuk.
We complete the classification of tight $4$-designs in Hamming association schemes $H(n,q)$, i.e., that of tight orthogonal arrays of strength $4$, which had been open since a result by Noda (1979). To do so, we construct an association scheme attached to a tight $4$-design in $H(n,q)$ and analyze its triple intersection numbers to conclude the non-existence in all open cases.
We determine the distance-regular graphs with diameter at least $3$ and $c_2\geq 2$ but without induced $K_{1,4}$-subgraphs.
J.H. Koolen and J. Park have proved a lower bound for intersection number $c_2$ of a distance-regular graph $Γ$. Moreover, they showed that the graph $Γ$ which attains the equality in this bound is a Terwilliger graph. We prove that $Γ$ is the icosahedron, the Doro graph or the Conway-Smith graph, if equality is attained and $c_2\ge 2$.