Mutual visibility in graphs
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 se...
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| Vydáno v: | Applied mathematics and computation Ročník 419; s. 126850 |
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| Jazyk: | angličtina |
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15.04.2022
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| ISSN: | 0096-3003 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 126850 |
| Author | Di Stefano, Gabriele |
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| Cites_doi | 10.1007/s00025-021-01438-x 10.1016/0020-0255(94)90060-4 10.1016/S0020-0255(98)10063-4 10.1016/j.akcej.2019.08.008 10.1016/j.ic.2016.09.005 10.3233/FI-2018-1748 10.1016/0095-8956(86)90043-2 10.1016/j.dam.2012.02.021 10.1017/S0004972718000473 10.1137/1.9780898719796 10.1016/j.tcs.2020.10.033 |
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| Snippet | 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... |
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| SubjectTerms | Computational complexity Graph classes Graph invariant Mutual visibility |
| Title | Mutual visibility in graphs |
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