Geodesic
Inverse problems of graph theory: generalized quadrangles
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 927-934.

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Graph $\Gamma_i$ for a distance-regular graph $\Gamma$ of diameter 3 can be strongly regular for $i=2$ or $i=3$. Finding parameters of $\Gamma_i$ by the intersection array of graph $\Gamma$ is a direct problem. Finding intersection array of graph $\Gamma$ by the parameters of $\Gamma_i$ is an inverse problem. Earlier direct and inverse problems have been solved by A.A. Makhnev, M.S. Nirova for $i=3$ and by A.A. Makhnev and D.V. Paduchikh for $i=2$. In this work the inverse problem has been solved in cases when graphs $\Gamma_2$, $\Gamma_3$, $\bar \Gamma_2$ or $\bar \Gamma_3$ are pseudo-geometric for generalized quadrangle. In particular, graphs $\Gamma_2$ and $\bar \Gamma_3$ are not to be a pseudo-geometric for generalized quadrangle.
Keywords: distance regular graph, graph $\Gamma$ with strongly regular graph $\Gamma_i$. 
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     title = {Inverse problems of graph theory: generalized quadrangles},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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A. A. Makhnev; M. S. Nirova. Inverse problems of graph theory: generalized quadrangles. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 927-934. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a71/

[1] A.E. Brouwer, A.M. Cohen, A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin–Heidelberg–New York, 1989 | MR | Zbl

[2] A. Makhnev, M. Nirova, “On distance-regular Shilla graphs”, Mat. Zametki, 103:5 (2018), 730–748 | DOI | MR

[3] A. Makhnev, D. Paduchikh, “Invers problems in graph theory”, Trudy Inst. Math. Mechaniki, 27, no. 3, 2018, 558–571 | MR

[4] A. Jurisic, J. Vidali, “Extremal 1-codes in distance-regular graphs of diameter 3”, Des. Codes Cryptogr., 65:1–2 (2012), 29–47 | DOI | MR | Zbl

[5] M. Nirova, “On distance-regular graphs $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$”, Sibirean Electr. Math. Reports, 15 (2018), 175–185 | MR