Point- and arc-reaching sets of vertices in a digraph
نویسندگان
چکیده
In a digraph D = (X,U) , not necessarily finite, an arc (x, y) ∈ U is reachable from a vertex u if there exists a directed walk W that originates from u and contains (x, y) . A subset S ⊆ X is an arc-reaching set of D if for every arc (x, y) there exists a diwalk W originating at a vertex u ∈ S and containing (x, y) . A minimal arc-reaching set is an arc-basis. S is a point-reaching set if for every vertex v there exists a diwalk W to v originating at a vertex u ∈ S . A minimal point-reaching set is a point-basis. We extend the results of Harary, Norman, and Cartwright on point-bases in finite digraphs to pointand arc-bases in infinite digraphs.
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