## Abstract In this article we study the product action of the direct product of automorphism groups of graphs. We generalize the results of Watkins [J. Combin Theory 11 (1971), 95β104], Nowitz and Watkins [Monatsh. Math. 76 (1972), 168β171] and W. Imrich [Israel J. Math. 11 (1972), 258β264], and w
Automorphism Groups of Covering Graphs
β Scribed by Norbert Seifter; Vladimir I. Trofimov
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 226 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0095-8956
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β¦ Synopsis
For a large class of finite Cayley graphs we construct covering graphs whose automorphism groups coincide with the groups of lifted automorphisms. As an application we present new examples of 1Γ2-transitive and 1-regular graphs.
π SIMILAR VOLUMES
Let 1 be a graph with almost transitive group Aut(1) and quadratic growth. We show that Aut(1) contains an almost transitive subgroup isomorphic to the free abelian group Z 2 .
## Abstract We investigate the properties of graphs whose automorphism group is the symmetric group. In particular, we characterize graphs on less than 2__n__ points with group __S~n~__, and construct all graphs on __n__ + 3 points with group __S~n~__. Graphs with 2__n__ or more points and group __
## Abstract Given a connected graph Ξ of order __n__ and diameter __d__, we establish a tight upper bound for the order of the automorphism group of Ξ as a function of __n__ and __d__, and determine the graphs for which the bound is attained. Β© 2011 Wiley Periodicals, Inc. J Graph Theory.
Let be a graph and let G be a subgroup of automorphisms of . Then G is said to be locally primitive on if, for each vertex v, the stabilizer G v induces a primitive group of permutations on the set of vertices adjacent to v. This paper investigates pairs G for which G is locally primitive on , G is