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This article is cited in 3 scientific papers (total in 3 papers)
Distance-transitive graphs admitting elations
A. A. Ivanov
Abstract:
A graph $\Gamma$ is called distance-transitive if, for every quadruple $x,y,u,v$ of its vertices such that $d(x,y)=d(u,v)$, there is an automorphism in the group $\operatorname{Aut}(\Gamma)$ which maps $x$ to $u$ and $y$ to $v$. The graph $\Gamma$ is called $s$-transitive if $\operatorname{Aut}(\Gamma)$ acts transitively on the set of paths of length $s$ but intransitively on the set of paths of length $s+1$ in the graph $\Gamma$. A nonunit automorphism a $\operatorname{Aut}(\Gamma)$ is called an elation if for some edge $\{x,y\}$ it fixes elementwise all the vertices adjacent to either $x$ or $y$. In this paper a complete description of distance-transitive graphs which are $s$-transitive for $s\geqslant2$ and whose automorphism groups contain elations is obtained.
Bibliography: 30 titles.
Received: 02.07.1987
Citation:
A. A. Ivanov, “Distance-transitive graphs admitting elations”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989), 971–1000; Math. USSR-Izv., 35:2 (1990), 307–335
Linking options:
https://www.mathnet.ru/eng/im1284https://doi.org/10.1070/IM1990v035n02ABEH000705 https://www.mathnet.ru/eng/im/v53/i5/p971
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Abstract page: | 333 | Russian version PDF: | 171 | English version PDF: | 6 | References: | 38 | First page: | 3 |
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