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Title: Inverse Problems in the Class of Q-Polynomial Graphs
Other Titles: Обратные задачи в классе Q-полиномиальных графов
Authors: Belousov, I. N.
Makhnev, A. A.
Issue Date: 2020
Publisher: Krasovskii Institute of Mathematics and Mechanics
Krasovskii Institute of Mathematics and Mechanics UB RAS
Citation: Belousov I. N. Inverse Problems in the Class of Q-Polynomial Graphs [Обратные задачи в классе Q-полиномиальных графов] / I. N. Belousov, A. A. Makhnev // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 3. — P. 14-22.
Abstract: In the class of distance-regular graphs Γ of diameter 3 with a pseudogeometric graph Γ3, feasible intersection arrays for the partial geometry were found for networks by Makhnev, Golubyatnikov, and Guo; for dual networks by Belousov and Makhnev; and for generalized quadrangles by Makhnev and Nirova. These authors obtained four infinite series of feasible intersection arrays of distance-regular graphs: {c2(u2 − m2) + 2c2m − c2 − 1, c2(u2 − m2), (c2 − 1)(u2 − m2) + 2c2m − c2; 1, c2, u2 − m2}, {mt, (t + 1)(m − 1), t + 1; 1, 1, (m − 1)t} for m ≤ t, {lt, (t − 1)(l − 1), t + 1; 1, t − 1, (l − 1)t}, and {a(p + 1), ap, a + 1; 1, a, ap}. We find all feasible intersection arrays of Q-polynomial graphs from these series. In particular, we show that, among these infinite families of feasible arrays, only two arrays ({7, 6, 5; 1, 2, 3} (folded 7-cube) and {191, 156, 153; 1, 4, 39}) correspond to Q-polynomial graphs. © 2020 Sverre Raffnsoe. All rights reserved.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85095715575
PURE ID: 13944697
ISSN: 0134-4889
metadata.dc.description.sponsorship: This work was supported by the Russian Foundation for Basic Research – the National Natural Science Foundation of China (project no. 20-51-53013_a).
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