On Vosperian and Superconnected Vertex-Transitive Digraphs
MetadataShow full item record
We investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We give a complete characterization of vosperian arc-transitive digraphs. It states that an arc-transitive strongly
connected digraph is vosperian if and only if it is irreducible. In particular, this is the case if the degree is coprime with the order of the digraph. We give also a complete characterization of vosperian Cayley digraphs and a complete characterization of irreducible superconnected Cayley digraphs. These two last characterizations extend the corresponding ones in Abelian Cayley digraphs and the ones in the undirected case.
Is part ofGraphs and Combinatorics, 2013, vol. 29, num. 2, p. 241-251
Showing items related by title, author, creator and subject.
López Masip, Susana-Clara (Elsevier, 2013)We give an upper bound for the size of non-trivial sets that have small boundary in a family of arc-transitive digraphs. We state the exact size for these sets in case of prime degree. We also give a lower bound for the ...
Hamidoune, Yahya Ould; Lladó, A.; López Masip, Susana-Clara (Wiley, 2011)A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex ...
López Masip, Susana-Clara; Muntaner Batle, F. A. (Springer, 2015)Figueroa-Centeno et al.  introduced the following product of digraphs let D be a digraph and let Γ be a family of digraphs such that V (F) = V for every F∈Γ . Consider any function h:E(D)→Γ . Then the product D⊗hΓ is ...