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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 175–185 (Mi semr908)  

This article is cited in 2 scientific papers (total in 2 papers)

Discrete mathematics and mathematical cybernetics

On distance-regular graph $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$

M. S. Nirova

Kabardino-Balkarian State University named after H.M. Berbekov, st. Chernyshevsky, 175, 360004, Nalchik, Russia

Abstract: It is investigated distance-regular graphs $\Gamma$ of diameter 3 with strongly regular graphs $\Gamma_2$ and $\Gamma_3$. If $\Gamma$ is antipodal graph then either $\Gamma$ is Taylor graph without triangles or $\bar \Gamma_2$ is pseudo-geometric graph for $GQ(r-1,c_2+1)$. If $\Gamma$ is primitive graph then $\Gamma$ has intersection array $\{r(c_2+1)+a_3,rc_2,a_3+1;1,c_2,r(c_2+1)\}$.
Last result gives intersection arrays in the case when $\Gamma_3$ is strongly regular graph without triangles. If $\mu(\Gamma_3)\le 11$, then $\Gamma$ has intersection array $\{14,10,3;1,5,12\}$, $\{119,100,15;1,20,105\}$ or $\{(r+5)((r+3)^2-3)/6,r(r+3)(r+8)/6,r+6;1,(r+3)(r+8)/6,r(r+5)(r+6)/6\}$, $r=4,6,10,16,19,24,28,40,46,52,58,60,70,79$.

Keywords: distance-regular graph, graph with strongly regular $\Gamma_2$ and $\Gamma_3$.

Funding Agency Grant Number
Russian Science Foundation 15-11-10025


DOI: https://doi.org/10.17377/semi.2018.15.017

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Bibliographic databases:

Document Type: Article
UDC: 519.17
MSC: 05C25
Received December 20, 2017, published March 1, 2018

Citation: M. S. Nirova, “On distance-regular graph $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$”, Sib. Èlektron. Mat. Izv., 15 (2018), 175–185

Citation in format AMSBIB
\Bibitem{Nir18}
\by M.~S.~Nirova
\paper On distance-regular graph $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 175--185
\mathnet{http://mi.mathnet.ru/semr908}
\crossref{https://doi.org/10.17377/semi.2018.15.017}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Makhnev, D. V. Paduchikh, “Obratnye zadachi v teorii distantsionno regulyarnykh grafov”, Tr. IMM UrO RAN, 24, no. 3, 2018, 133–144  mathnet  crossref  elib
    2. A. A. Makhnev, M. S. Nirova, “Obratnye zadachi v teorii grafov: obobschennye chetyrekhugolniki”, Sib. elektron. matem. izv., 15 (2018), 927–934  mathnet  crossref
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