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Title:Variety of general position problems in graphs
Authors:ID Tian, Jing (Author)
ID Klavžar, Sandi (Author)
Files:.pdf PDF - Presentation file, download (377,60 KB)
MD5: 6B93719702121058EF4162871595D6E9
 
URL URL - Source URL, visit https://link.springer.com/article/10.1007/s40840-024-01788-z
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:Let X be a vertex subset of a graph G. Then u,v∈V(G) are X-positionable if V(P)∩X⊆{u,v} holds for any shortest u,v-path P. If each two vertices from X are X-positionable, then X is a general position set. The general position number of G is the cardinality of a largest general position set of G and has been already well investigated. In this paper a variety of general position problems is introduced based on which natural pairs of vertices are required to be X-positionable. This yields the total (resp. dual, outer) general position number. It is proved that the total general position sets coincide with sets of simplicial vertices, and that the outer general position sets coincide with sets of mutually maximally distant vertices. It is shown that a general position set is a dual general position set if and only if its complement is convex. Several sufficient conditions are presented that guarantee that a given graph has no dual general position set. The total general position number, the outer general position number, and the dual general position number of arbitrary Cartesian products are determined.
Keywords:general position, total general position, outer general position, dual general position, Cartesian product of graphs, strong resolving graph, convex subgraph
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2025
Year of publishing:2025
Number of pages:14 str.
Numbering:Vol. 48, iss. 1, [article no.] 5
PID:20.500.12556/DiRROS-20785 New window
UDC:519.17
ISSN on article:0126-6705
DOI:10.1007/s40840-024-01788-z New window
COBISS.SI-ID:213851395 New window
Note:
Publication date in DiRROS:07.11.2024
Views:255
Downloads:203
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TIAN, Jing and KLAVŽAR, Sandi, 2025, Variety of general position problems in graphs. Bulletin of the Malaysian Mathematical Sciences Society [online]. 2025. Vol. 48, no. 1,  5. [Accessed 7 April 2025]. DOI 10.1007/s40840-024-01788-z. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=20785
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Record is a part of a journal

Title:Bulletin of the Malaysian Mathematical Sciences Society
Shortened title:Bull. Malays. Math. Sci. Soc.
Publisher:Springer Nature, Malaysian Mathematical Society.
ISSN:0126-6705
COBISS.SI-ID:515781657 New window

Document is financed by a project

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0297
Name:Teorija grafov
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0355
Name:Prirejanja, transverzale in hipergrafi
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0285
Name:Metrični problemi v grafih in hipergrafih

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:splošna lega, celotna splošna lega, zunanja splošna lega, dualna splošna lega, kartezični produkt grafov, krepki solventni graf, konveksen podgraf


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