Abstract:In this paper we generalise the notion of visibility from a point in an integer lattice to the setting of graph theory. For a vertex x of a connected graph G, we say that a set S ⊆ V (G) is an x-position set if for any y ∈ S the shortest x, y-paths in G contain no point of S \ {y}. We investigate the largest and smallest orders of maximum x-position sets in graphs, determining these numbers for common classes of graphs and giving bounds in terms of the girth, vertex degrees, diameter and radius. Finally we dis… Show more
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