A. A. Makhnev, D. V. Paduchikh, “Exceptional strongly regular graphs with eigenvalue 3”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 167–174; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 93

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 4, Pages 167–174 (Mi timm1010)

This article is cited in 11 scientific papers (total in 11 papers)

Exceptional strongly regular graphs with eigenvalue 3

A. A. Makhnev^ab, D. V. Paduchikh^a

^a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Full-text PDF (154 kB) Citations (11)

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Abstract: A strongly regular graph

Γ

$\Gamma$ with eigenvalue

m - 1

$m-1$ is called exceptional if it does not belong to the following list: (1) the union of isolated

m

$m$ -cliques, (2) a pseudogeometric graph for

p G_{t} (t + m - 1, t)

$pG_t(t+m-1,t)$ , (3) the completion to a pseudogeometric graph for

p G_{m} (s, m - 1)

$pG_{m}(s,m-1)$ , (4) a graph in the half case with parameters

(4 μ + 1, 2 μ, μ - 1, μ)

$(4\mu+1,2\mu,\mu-1,\mu)$ ,

\sqrt{4 μ + 1} = m - 1

$\sqrt{4\mu+1}=m-1$ . We find parameters of exceptional strongly regular graphs with nonleading eigenvalue 3.

Keywords: strongly regular graph, eigenvalue of a graph.

Received: 17.06.2013

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 287, Issue 1, Pages 93–101
DOI: https://doi.org/10.1134/S0081543814090090

Bibliographic databases:

Document Type: Article

UDC: 519.17

Language: Russian

Citation: A. A. Makhnev, D. V. Paduchikh, “Exceptional strongly regular graphs with eigenvalue 3”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 167–174; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 93–101

Citation in format AMSBIB

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\paper Exceptional strongly regular graphs with eigenvalue~3

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\vol 19

\issue 4

\pages 167--174

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\jour Proc. Steklov Inst. Math. (Suppl.)

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\pages 93--101

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Linking options:

https://www.mathnet.ru/eng/timm1010

https://www.mathnet.ru/eng/timm/v19/i4/p167

This publication is cited in the following 11 articles:

A. K. Gutnova, A. A. Makhnev, “On Graphs Whose Local Subgraphs Are Pseudogeometric For $GQ(4, t)$ ”, Dokl. Math., 91:3 (2015), 371–375
K. S. Efimov, A. A. Makhnev, “on Graphs With in Strongly Regular Local Subgraphs Having Parameters $(88,27,6,9)$ ”, Dokl. Math., 91:1 (2015), 80–83
Makhnev A.A., Paduchikh D.V., “On Extensions of Small Strongly Regular Graphs With Eigenvalue 3”, Dokl. Math., 92:1 (2015), 482–486
A. A. Makhnev, “Silno regulyarnye grafy so vtorym sobstvennym znacheniem 4 i ikh rasshireniya”, Tr. In-ta matem., 23:2 (2015), 82–87
A. A. Makhnev, D. V. Paduchikh, “Distance regular graphs in which local subgraphs are strongly regular graphs with the second eigenvalue at most 3”, Dokl. Math., 92:2 (2015), 568
A. A. Makhnev, M. S. Samoilenko, “Automorphisms of a Strongly Regular Graph With Parameters (276,75,10,24)”, Dokl. Math., 90:1 (2014), 485–488
A. A. Makhnev, A. A. Tokbaeva, “On Graphs With Strongly Regular Local Subgraphs With Parameters (196,45,4,12)”, Dokl. Math., 89:3 (2014), 276–278
Kagazezheva A.M., Makhnev A.A., “On Graphs With Strongly Regular Local Subgraphs With Parameters (111,30,5,9) Or (169,42,5,12)”, Dokl. Math., 89:3 (2014), 283–286
Makhnev A.A., Paduchikh D.V., “On Extensions of Exceptional Strongly Regular Graphs With Eigenvalue 3”, Dokl. Math., 89:3 (2014), 354–358
Belousov I.N., Makhnev A.A., “On Extensions of Strongly Regular Graphs Without Triangles With Eigenvalue 3”, Dokl. Math., 90:1 (2014), 395–398
Makhnev A.A., Paduchikh D.V., “On Graphs Whose Local Subgraphs Are Strongly Regular With Parameters (144,39,6,12)”, Dokl. Math., 89:2 (2014), 235–238

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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