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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 5, Pages 971–1000 (Mi izv1284)

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.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:2, 307–335

Bibliographic databases:

UDC: 519.4
MSC: Primary 05C25; Secondary 20F32

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

Citation in format AMSBIB
\Bibitem{Iva89} \by A.~A.~Ivanov \paper Distance-transitive graphs admitting elations \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 5 \pages 971--1000 \mathnet{http://mi.mathnet.ru/izv1284} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1024451} \zmath{https://zbmath.org/?q=an:0723.05069|0706.05026} \transl \jour Math. USSR-Izv. \yr 1990 \vol 35 \issue 2 \pages 307--335 \crossref{https://doi.org/10.1070/IM1990v035n02ABEH000705}