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- W2903169371 abstract "We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph $Lambda$ and a assigned to each orbit of Aut($Lambda$), there exists a unique lobe-transitive graph $Gamma$ of connectivity 1 whose lobes are copies of $Lambda$ and is consistent with the given code at every vertex of $Gamma$. These results lead to necessary and sufficient conditions for a graph of connectivity $1$ to be edge-transitive and to be arc-transitive. Countable graphs of connectivity 1 the action of whose automorphism groups is, respectively, vertex-transitive, primitive, regular, Cayley, and Frobenius had been previously characterized in the literature." @default.
- W2903169371 created "2018-12-11" @default.
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- W2903169371 date "2018-11-29" @default.
- W2903169371 modified "2023-09-27" @default.
- W2903169371 title "Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1" @default.
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- W2903169371 hasPublicationYear "2018" @default.
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