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J. Sib. Fed. Univ. Math. Phys., 2009, Volume 2, Issue 1, Pages 63–77 (Mi jsfu52)  

This article is cited in 2 scientific papers (total in 3 papers)

Amply Regular Graphs with $b_1=6$

Konstantin S. Efimov, Alexander A. Makhnev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The unnoriented graph with $v$ verteces of valency $k$, such that every edge belongs to $\lambda$ triangles, is called an edge regular graph with the parameters $(v,k,\lambda)$. Let $b_1=k-\lambda-1$. In [1] it is proved that a connected edge regular graph with $b_1=1$ is either a polygon or a complete multipart graph all of whose parts have order 2. Edge regular graphs with $b_1\le5$ have been studied in previous work. In the present paper we investigate amply regular graphs with $b_1=6$.

Keywords: amply regular graph, unoriented graph.

Full text: PDF file (386 kB)
References: PDF file   HTML file
UDC: 519.17
Received: 10.09.2008
Received in revised form: 15.12.2008
Accepted: 15.01.2009

Citation: Konstantin S. Efimov, Alexander A. Makhnev, “Amply Regular Graphs with $b_1=6$”, J. Sib. Fed. Univ. Math. Phys., 2:1 (2009), 63–77

Citation in format AMSBIB
\Bibitem{EfiMak09}
\by Konstantin~S.~Efimov, Alexander~A.~Makhnev
\paper Amply Regular Graphs with $b_1=6$
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2009
\vol 2
\issue 1
\pages 63--77
\mathnet{http://mi.mathnet.ru/jsfu52}
\elib{http://elibrary.ru/item.asp?id=11716611}


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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. K. S. Efimov, A. A. Makhnev, “O vpolne regulyarnykh grafakh s $k=11$, $\lambda=4$”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 83–92  mathnet
    2. K. S. Efimov, “Classification of amply regular graphs with $b_1=6$”, Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 46–55  mathnet  crossref  isi  elib
    3. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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