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 Sib. Èlektron. Mat. Izv., 2017, Volume 14, Pages 367–387 (Mi semr789)

Discrete mathematics and mathematical cybernetics

Claw-free strictly Deza graphs

V. V. Kabanova, A. V. Mityaninab

a Krasovskii Institute of Mathematics and Mechanics UB RAS, ul. S. Kovalevskoy, 16, 620990, Yekaterinburg, Russia
b Chelyabinsk State University, ul. Br. Kashirinyh, 129, 454000, Chelyabinsk, Russia

Abstract: A Deza graph with parameters $(v,k,b,a)$ is a $k$-regular graph, which has exactly $v$ vertices and any two distinct vertices have either $a$ or $b$ common neighbors. A strictly Deza graph is a Deza graph of diameter $2$ that is not strongly regular. A claw-free graph is a graph in which no induced subgraph is a complete bipartite graph $K_{1,3}$. We proved if graph $G$ is a claw-free strictly Deza graph which contains a $3$-coclique then $G$ is either an $4 \times n$-lattice, where $n > 2$, $n \neq 4$, or the $2$-extension of the $3 \times 3$-lattice, or two strictly Deza graphs with the parameters $(9,4,2,1)$, or two strictly Deza graphs with the parameters $(12,6,3,2)$, or a Deza line graph with the parameters $(20,6,2,1)$.

Keywords: strictly Deza graphs, claw-free graphs.

DOI: https://doi.org/10.17377/semi.2017.14.030

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Bibliographic databases:

UDC: 519.172.4
MSC: 05C25
Received October 21, 2016, published April 6, 2017
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Citation: V. V. Kabanov, A. V. Mityanina, “Claw-free strictly Deza graphs”, Sib. Èlektron. Mat. Izv., 14 (2017), 367–387

Citation in format AMSBIB
\Bibitem{KabMit17} \by V.~V.~Kabanov, A.~V.~Mityanina \paper Claw-free strictly Deza graphs \jour Sib. \Elektron. Mat. Izv. \yr 2017 \vol 14 \pages 367--387 \mathnet{http://mi.mathnet.ru/semr789} \crossref{https://doi.org/10.17377/semi.2017.14.030} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000407792200034} `