Koolen–Bang finiteness conjecture for geometric distance-regular graphs

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Let m≥2m \geq 2 be a fixed integer. A distance-regular graph is coconnected if it is not a disjoint union of complete graphs. Let ϕ1\phi_1 and τ2\tau_2 be the clique parameters associated with a geometric distance-regular graph. Koolen–Bang's finiteness conjecture. There are only finitely many coconnected geometric distance-regular graphs with smallest eigenvalue −m-m and ϕ1≤τ2−2\phi_1 \leq \tau_2 - 2. This conjecture is attributed in the source to Koolen and Bang and remains open.

References

Primary source

Chenhui Lv and Jack H. Koolen, “On the characterization of geometric distance-regular graphs”, arXiv:2601.10330 (2026).

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