The automorphism-group of an infinite graph acts in a natural way on the set of d-fibers (components of the set of rays with respect to the Hausdorff metric). For connected, locally finite, almost transitive graphs the kernel of this action is proved to be the group of bounded automorphisms. This co
A characterization of locally finite vertex-transitive graphs
β Scribed by Carsten Thomassen
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 200 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0095-8956
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## Abstract We present necessary and sufficient conditions for a graph to admit a vertexβtransitive embedding on some surface. Β© 2007 Wiley Periodicals, Inc. J Graph Theory 55: 233β248, 2007
Let G be a group acting symmetrically on a graph 2, let G, be a subgroup of G minimal among those that act symmetrically on 8, and let G2 be a subgroup of G, maximal among those normal subgroups of GI which contain no member except 1 which fixes a vertex of Z. The most precise result of this paper i
The maximum genus of all vertex-transitive graphs is computed. It is proved that a k-valent vertex-transitive graph of girth g is upper-embeddable whenever k 3 4 or g 2 4. Non-upper-embeddable vertex-transitive graphs are characterized. A particular attention is paid to Cayley graphs. Groups for wh
A graph is vertex-transitive or symmetric if its automorphism group acts transitively on vertices or ordered adjacent pairs of vertices of the graph, respectively. Let G be a finite group and S a subset of G such that 1 / β S and S = {s -1 | s β S}. The Cayley graph Cay(G, S) on G with respect to S