Variety of mutual-visibility problems in hypercubes
Abstract
Let be a graph and . Vertices are -visible if there exists a shortest -path of that does not pass through any vertex of . We say that is a mutual-visibility set if each pair of vertices of is -visible, while the size of any largest mutual-visibility set of is the mutual-visibility number of . If some additional combinations for pairs of vertices are required to be -visible, we obtain the total (every are -visible), the outer (every and every are -visible), and the dual (every are -visible) mutual-visibility set of . The cardinalities of the largest of the above defined sets are known as the total, the outer, and the dual mutual-visibility number of , respectively. We present results on the variety of mutual-visibility problems in hypercubes.
Cite
@article{arxiv.2405.05650,
title = {Variety of mutual-visibility problems in hypercubes},
author = {Danilo Korže and Aleksander Vesel},
journal= {arXiv preprint arXiv:2405.05650},
year = {2024}
}