A walk W between vertices u and v of a graph G is called a {\em tolled walk between u and v} if u, as well as v, has exactly one neighbour in W. A set S⊆V(G) is {\em toll convex} if the vertices contained in any tolled walk between two vertices of S are contained in S. The {\em toll convex hull of S} is the minimum toll convex set containing~S. The {\em toll hull number of G} is the minimum cardinality of a set S such that the toll convex hull of S is V(G). The main contribution of this work is an algorithm for computing the toll hull number of a general graph in polynomial time.
Cite
@article{arxiv.1905.00109,
title = {Computing the hull number in toll convexity},
author = {Mitre C. Dourado},
journal= {arXiv preprint arXiv:1905.00109},
year = {2020}
}