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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.
Received October 21, 2016, published April 6, 2017
Citation:
V. V. Kabanov, A. V. Mityanina, “Claw-free strictly Deza graphs”, Sib. Èlektron. Mat. Izv., 14 (2017), 367–387
Linking options:
https://www.mathnet.ru/eng/semr789 https://www.mathnet.ru/eng/semr/v14/p367
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Abstract page: | 290 | Full-text PDF : | 70 | References: | 43 |
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