Topological graph theory
A note on the growth of transitive graphs
Discrete Mathematics - Proceedings of the Oberwolfach Meeting "Kombinatorik," January 19-25, 1986
An infinite highly arc-transitive digraph
European Journal of Combinatorics
Lifting graph automorphisms by voltage assignments
European Journal of Combinatorics
A Conjecture Concerning a Limit of Non-Cayley Graphs
Journal of Algebraic Combinatorics: An International Journal
Descendants in highly arc transitive digraphs
Discrete Mathematics
Bridging semisymmetric and half-arc-transitive actions on graphs
European Journal of Combinatorics
Highly arc transitive digraphs: reachability, topological groups
European Journal of Combinatorics
On geometric properties of directed vertex-symmetric graphs
European Journal of Combinatorics
An infinite family of half-arc-transitive graphs with universal reachability relation
European Journal of Combinatorics
Descendant-homogeneous digraphs
Journal of Combinatorial Theory Series A
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In this paper we study reachability relations on vertices of digraphs, informally defined as follows. First, the weight of a walk is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed in the direction opposite to their orientation. Then, a vertex u is R"k^+-related to a vertex v if there exists a 0-weighted walk from u to v whose every subwalk starting at u has weight in the interval [0,k]. Similarly, a vertex u is R"k^--related to a vertex v if there exists a 0-weighted walk from u to v whose every subwalk starting at u has weight in the interval [-k,0]. For all positive integers k, the relations R"k^+ and R"k^- are equivalence relations on the vertex set of a given digraph. We prove that, for transitive digraphs, properties of these relations are closely related to other properties such as having property Z, the number of ends, growth conditions, and vertex degree.