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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 6, Pages 95–114 (Mi izv667)  

This article is cited in 3 scientific papers (total in 4 papers)

On a class of coedge regular graphs

A. A. Makhnev, D. V. Paduchikh

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

Abstract: We study graphs in which $\lambda(a,b)=\lambda_1,\lambda_2$ for every edge $\{a,b\}$ and all $\mu$-subgraphs are 2-cocliques. We give a description of connected edge-regular graphs for $k\geqslant(b_1^2+3b_1-4)/2$. In particular, the following examples confirm that the inequality $k>b_1(b_1+3)/2$ is a sharp bound for strong regularity: the $n$-gon, the icosahedron graph, the graph in $\operatorname{MP}(6)$ and the distance-regular graph of diameter 4 with intersection massive $\{x,x-1,4,1;1,2,x-1,x\}$, which is an antipodal 3-covering of the strongly regular graph with parameters $((x+2)(x+3)/6,x,0,6)$.

DOI: https://doi.org/10.4213/im667

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English version:
Izvestiya: Mathematics, 2005, 69:6, 1169–1187

Bibliographic databases:

UDC: 519.14
MSC: 05C75, 05E30
Received: 25.05.2004

Citation: A. A. Makhnev, D. V. Paduchikh, “On a class of coedge regular graphs”, Izv. RAN. Ser. Mat., 69:6 (2005), 95–114; Izv. Math., 69:6 (2005), 1169–1187

Citation in format AMSBIB
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\paper On a~class of coedge regular graphs
\jour Izv. RAN. Ser. Mat.
\yr 2005
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\pages 95--114
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\vol 69
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\pages 1169--1187
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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. Konstantin S. Efimov, Aleksandr A. Makhnev, “Vpolne regulyarnye grafy s $b_1=6$”, Zhurn. SFU. Ser. Matem. i fiz., 2:1 (2009), 63–77  mathnet  elib
    2. Makhnev A.A., Paduchikh D.V., “On graphs in which each $\mu$-subgraph is a pentagon”, Dokl. Math., 81:2 (2010), 251–254  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. V. V. Kabanov, A. V. Mityanina, “Strictly Deza line graphs”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S78–S90  mathnet  crossref  isi  elib
    4. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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