@Article{Tian2026,
author = "Tian, Jing and Bujtás, Csilla and Klavžar, Sandi",
title = "Independent mutual-visibility sets and distance edge-critical graphs",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "5",
pages = "773--790",
doi = "https://doi.org/10.7494/OpMath.202609091",
url = "https://doi.org/10.7494/OpMath.202609091",
abstract = "In this paper, connections between independent sets and the variety of mutual-visibility sets are studied. It is proved that every outer mutual-visibility set of a graph is independent if and only if the graph is distance edge-critical. Several constructions yielding distance edge-critical graphs are given. Graphs in which every independent set is a total mutual-visibility or a dual mutual-visibility set are characterized, as well as graphs in which every total mutual-visibility set is independent. Along the way the total mutual-visibility number of some graphs derived from fullerenes is determined. Diameter four graphs in which every independent set is a mutual-visibility set are characterized. It is proved that determining the maximum cardinality of an independent mutual-visibility set and deciding whether it equals the independence number of a graph are NP-hard problems, and the same is true for independent total, outer and dual mutual-visibility sets.",
keywords = "mutual-visibility set, independent set, distance edge-critical graph, dense diamond graph, computational complexity",
issn = "1232-9274"
}