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Resolvability and convexity properties in the Sierpiński product of graphs
ID
Henning, Michael A.
(
Author
),
ID
Klavžar, Sandi
(
Author
),
ID
Yero, Ismael G.
(
Author
)
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MD5: 074DE5ECE31FEB8F337B464DEC07BA72
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https://link.springer.com/article/10.1007/s00009-023-02544-6
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Abstract
Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $gg'$ of $G$ there is an edge between copies $gH$ and $g'H$ of $H$ associated with the vertices $g$ and $g'$ of $G$, respectively, of the form $(g,f(g'))(g',f(g))$. The Sierpiński metric dimension and the upper Sierpiński metric dimension of two graphs are determined. Closed formulas are determined for Sierpiński products of trees, and for Sierpiński products of two cycles where the second factor is a triangle. We also prove that the layers with respect to the second factor in a Sierpiński product graph are convex.
Language:
English
Keywords:
Sierpiński product of graphs
,
metric dimension
,
trees
,
convex subgraph
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Version of Record
Year:
2024
Number of pages:
17 str.
Numbering:
Vol. 21, iss. 1, art. 3
PID:
20.500.12556/RUL-152589
UDC:
519.17
ISSN on article:
1660-5446
DOI:
10.1007/s00009-023-02544-6
COBISS.SI-ID:
172901379
Publication date in RUL:
29.11.2023
Views:
852
Downloads:
27
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Record is a part of a journal
Title:
Mediterranean journal of mathematics
Shortened title:
Mediterr. j. math.
Publisher:
Springer Nature
ISSN:
1660-5446
COBISS.SI-ID:
13561433
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Secondary language
Language:
Slovenian
Keywords:
Sierpinskijev produkt grafov
,
metrična dimenzija
,
drevesa
,
konveksni podgrafi
Projects
Funder:
Other - Other funder or multiple funders
Funding programme:
South Africa, National Research Foundation
Project number:
129265
Funder:
Other - Other funder or multiple funders
Funding programme:
University of Johannesburg
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0297
Name:
Teorija grafov
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-2452
Name:
Strukturni, optimizacijski in algoritmični problemi v geometrijskih in topoloških predstavitvah grafov
Funder:
ARRS - Slovenian Research Agency
Project number:
N1-0285
Name:
Metrični problemi v grafih in hipergrafih
Funder:
Other - Other funder or multiple funders
Funding programme:
Spain, Ministry of Science and Innovation
Project number:
PID2019-105824GB-I00
Funder:
Other - Other funder or multiple funders
Funding programme:
Spain, Ministerio de Educación, Cultura y Deporte, José Castillejo program for young researchers
Project number:
CAS21/00100
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