Variety of mutual-visibility problems in hypercubes

被引：0

作者：

Korze, Danilo ^{[1
]}

Vesel, Aleksander ^{[2
]}

机构：

[1] Univ Maribor, Fac Elect Engn & Comp Sci, Koroska Cesta 46, SI-2000 Maribor, Slovenia

[2] Univ Maribor, Fac Nat Sci & Math, Koroska Cesta 160, SI-2000 Maribor, Slovenia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2025年 / 491卷

关键词：

Mutual visibility; Hypercube; Binary code; ROBOTS;

D O I：

10.1016/j.amc.2024.129218

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph and M c V(G). Vertices x, y E Mare M-visible if there exists a shortest x, y-path of G that does not pass through any vertex of M \ {x,y}. We say that M is a mutual-visibility set if each pair of vertices of M is M-visible, while the size of any largest mutual-visibility set of G is the mutual-visibility number of G. If some additional combinations for pairs of vertices x, y are required to be M-visible, we obtain the total (every x, y E V(G) are M-visible), the outer (every x E M and every y E V(G) \ M are M-visible), and the dual (every x, y E V(G) \ M are M-visible) mutual-visibility set of G. The cardinalities of the largest of the above defined sets are known as the total, the outer, and the dual mutual-visibility number of G, respectively. We present results on the variety of mutual-visibility problems in hypercubes.

引用

页数：10