Highly arc transitive diagraphs
European Journal of Combinatorics
Vertex-transitive graphs and accessibility
Journal of Combinatorial Theory Series B
Distance-transitivity in infinite graphs
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
A census of infinite distance-transitive graphs
Proceedings of the conference on Discrete metric spaces
Descendants in highly arc transitive digraphs
Discrete Mathematics
2-Arc-transitive regular covers of complete graphs Having the covering transformation group Zp3
Journal of Combinatorial Theory Series B
Finite symmetric graphs with two-arc transitive quotients
Journal of Combinatorial Theory Series B
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A graph @C is k-CS-transitive, for a positive integer k, if for any two connected isomorphic induced subgraphs A and B of @C, each of size k, there is an automorphism of @C taking A to B. The graph is called k-CS-homogeneous if any isomorphism between two connected induced subgraphs of size k extends to an automorphism. We consider locally-finite infinite k-CS-homogeneous and k-CS-transitive graphs. We classify those that are 3-CS-transitive (respectively homogeneous) and have more than one end. In particular, the 3-CS-homogeneous graphs with more than one end are precisely Macpherson's locally finite distance transitive graphs. The 3-CS-transitive but non-homogeneous graphs come in two classes. The first are line graphs of semiregular trees with valencies 2 and m, while the second is a class of graphs built up from copies of the complete graph K"4, which we describe.