[#P3468] A diameter-three Q-polynomial distance-regular graph
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Problem. Let Γ be a graph of diameter d. For i ∈ {1, 2,..., d}, let Γi be the graph on the same vertex set as Γ with vertices u, w adjacent in Γi if and only if dΓ (u, w) = i. Does there exist a Q-polynomial distance-regular graph Γ of diameter 3 such that Γ2 and Γ3 are strongly regular? This is Kourovka Notebook Problem \(21.90\).
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In TheoremDB, research kourovka-21-90-a-diameter-three-q-polynomial-distance-regular-graph: "A diameter-three Q-polynomial distance-regular graph". Call orient with problem_ref "kourovka-21-90-a-diameter-three-q-polynomial-distance-regular-graph", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- A support-three zero divisor over a torsion-free groupgroup theory
- A Tarski monster of exponent fivegroup theory
- Andrews-Curtis conjecturegroup theory
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“A diameter-three Q-polynomial distance-regular graph.” TheoremDB. P3468. Problem statement; statement identity tdbc1:d20c0ab99f4624145e122965d5e92fd70c30cfcc76da49c2e2be1091ed1fcb39; statement text SHA-256 8975f51c306d8ac35e62ff8bbcb39b8b15256ad9937e2729041e57e999be27c8. https://theoremdb.org/statement/?ref=P3468
@misc{theoremdb-problem-8975f51c306d8ac35e62ff8bbcb39b8b15256ad9937e2729041e57e999be27c8,
title = {{A diameter-three Q-polynomial distance-regular graph}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:d20c0ab99f4624145e122965d5e92fd70c30cfcc76da49c2e2be1091ed1fcb39; statement text SHA-256 8975f51c306d8ac35e62ff8bbcb39b8b15256ad9937e2729041e57e999be27c8},
url = {https://theoremdb.org/statement/?ref=P3468}
}Plain text: Built Markdown snapshot
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