| Title: | Mutual-visibility in strong products of graphs via total mutual-visibility |
|---|
| Authors: | ID Cicerone, Serafino (Author)
ID Di Stefano, Gabriele (Author)
ID Klavžar, Sandi (Author)
ID Yero, Ismael G. (Author) |
|---|
| Files: |  PDF - Presentation file, download (618,95 KB)
MD5: 9F622F07C0DA768E2A9136C1680C2F92
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0166218X24002907
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility set if each pair of vertices from $X$ is connected by a geodesic with no internal vertex in $X$. The mutual-visibility number $\mu(G)$ of $G$ is the cardinality of a largest mutual-visibility set. In this paper, the mutual-visibility number of strong product graphs is investigated. As a tool for this, total mutual-visibility sets are introduced. Along the way, basic properties of such sets are presented. The (total) mutual-visibility number of strong products is bounded from below in two ways, and determined exactly for strong grids of arbitrary dimension. Strong prisms are studied separately and a couple of tight bounds for their mutual-visibility number are given. |
|---|
| Keywords: | mutual-visibility set, mutual-visibility number, total mutual-visibility set, strong product of graphs |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.12.2024 |
|---|
| Year of publishing: | 2024 |
|---|
| Number of pages: | str. 136-146 |
|---|
| Numbering: | Vol. 358 |
|---|
| PID: | 20.500.12556/DiRROS-20505  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 0166-218X |
|---|
| DOI: | 10.1016/j.dam.2024.06.038 |
|---|
| COBISS.SI-ID: | 201822467 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 02.10.2024 |
|---|
| Views: | 220 |
|---|
| Downloads: | 105 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
