Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 206–216
DOI: https://doi.org/10.33048/semi.2019.16.012
(Mi semr1050)
 

This article is cited in 4 scientific papers (total in 4 papers)

Discrete mathematics and mathematical cybernetics

Distance-regular graph with intersection array $\{105,72,24;1,12,70\}$ does not exist

I. N. Belousov, A. A. Makhnev

N.N. Krasovskii Institute of Mathematics and Mechanics of UB RAS, 16, S.Kovalevskaya str., Yekaterinburg, 620990, Russia
Full-text PDF (173 kB) Citations (4)
References:
Abstract: Distance-regular graph $\Gamma$ of diameter 3 is called Shilla graph if $\Gamma$ containes the second eigenvalue $\theta_1=a_3$. In this case $a=a_3$ devides $k$ and we set $b=b(\Gamma)=k/a$. Koolen and Park obtained the list of intersection arrays for Shilla graphs with $b=3$. A. Brouwer with coauthors proved that graph with intersection array $\{27,20,10;1,2,18\}$ does not exist. $Q$-polinomial Shilla graph with $b=3$ has intersection array $\{42,30,12;1,6,28\}$ or $\{105,72,24;1,12,70\}$. Early authors proved that graph with intersection array $\{42,30,12;1,6,28\}$ does not exist.
We prove that graph with intersection array $\{105,72,24;1,12,70\}$ does not exist.
Keywords: distance-regular graph, Shilla graph, triple intersection numbers.
Received December 18, 2018, published February 8, 2019
Bibliographic databases:
Document Type: Article
UDC: 519.17
MSC: 05C25
Language: Russian
Citation: I. N. Belousov, A. A. Makhnev, “Distance-regular graph with intersection array $\{105,72,24;1,12,70\}$ does not exist”, Sib. Èlektron. Mat. Izv., 16 (2019), 206–216
Citation in format AMSBIB
\Bibitem{BelMak19}
\by I.~N.~Belousov, A.~A.~Makhnev
\paper Distance-regular graph with intersection array $\{105,72,24;1,12,70\}$ does not exist
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 206--216
\mathnet{http://mi.mathnet.ru/semr1050}
\crossref{https://doi.org/10.33048/semi.2019.16.012}
Linking options:
  • https://www.mathnet.ru/eng/semr1050
  • https://www.mathnet.ru/eng/semr/v16/p206
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:363
    Full-text PDF :167
    References:27
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024