Janoš Vidali: The Terwilliger polynomial of classical distance-regular graphs with b = 2
Datum objave: 23. 11. 2019
Seminar za diskretno matematiko
Torek, 26. 11. 2019, od 10h do 12h, Plemljev seminar, Jadranska 19
Povzetek. Let Γ be a Q-polynomial distance-regular graph with diameter
at least 3. In his lecture notes on the Terwilliger algebra (1993,
edited by H. Suzuki), P. Terwilliger implicitly showed that there exists
a quartic polynomial T, which only depends on the intersection numbers of Γ, such that for each local graph Γ(x) at vertex x, T(η) ≥ 0 holds for all non-principal eigenvalues η of Γ(x). We call the polynomial T the Terwilliger polynomial.
Recently,
A. Gavrilyuk and J. Koolen have used the Terwilliger polynomial to
classify pseudo-partition graphs with diameter at least 3 and to
characterize the graphs of bilinear forms H_2(d, d) by their parameters. We will generalize their technique to study distance-regular graphs with classical parameters (d,
2, α, β) and obtain many nonexistence results, mostly for the
parameters with α=1, which include the bilinear forms graphs and pass
all standard feasibility conditions when β is large enough.