Mutual visibility in graphs

Gabriele Di Stefano

Applied Mathematics and Computation, 2022, vol. 419, issue C

Abstract: Let G=(V,E) be a graph and P⊆V a set of points. Two points are mutually visible if there is a shortest path between them without further points. P is a mutual-visibility set if its points are pairwise mutually visible. The mutual-visibility number of G is the size of any largest mutual-visibility set. In this paper we start the study about this new invariant and the mutual-visibility sets in undirected graphs. We introduce the Mutual-Visibility problem which asks to find a mutual-visibility set with a size larger than a given number. We show that this problem is NP-complete, whereas, to check whether a given set of points is a mutual-visibility set is solvable in polynomial time. Then we study mutual-visibility sets and mutual-visibility numbers on special classes of graphs, such as block graphs, trees, grids, tori, complete bipartite graphs, cographs. We also provide some relations of the mutual-visibility number of a graph with other invariants.

Keywords: Mutual visibility; Graph invariant; Computational complexity; Graph classes (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:419:y:2022:i:c:s0096300321009334

DOI: 10.1016/j.amc.2021.126850

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