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THE GENERAL POSITION NUMBER OF THE CARTESIAN PRODUCT OF TWO TREES

Part of: Graph theory

Published online by Cambridge University Press:  04 December 2020

JING TIAN Open the ORCID record for JING TIAN [Opens in a new window] ,
KEXIANG XU Open the ORCID record for KEXIANG XU [Opens in a new window]  and
SANDI KLAVŽAR Open the ORCID record for SANDI KLAVŽAR [Opens in a new window]
JING TIAN
Affiliation:
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu210016, PR China e-mail: [email protected]
KEXIANG XU*
Affiliation:
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu210016, PR China
SANDI KLAVŽAR
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia; Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest path. In this paper it is proved that the general position number is additive on the Cartesian product of two trees.

Keywords

Cartesian productgeneral position numbergeneral position settrees

MSC classification

Primary: 05C05: Trees
Secondary: 05C12: Distance in graphs 05C35: Extremal problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 1 , August 2021 , pp. 1 - 10
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Kexiang Xu is supported by NNSF of China (grant no. 11671202 and the China–Slovene bilateral grant 12-9). Sandi Klavžar acknowledges financial support from the Slovenian Research Agency (research core funding P1-0297, projects J1-9109, J1-1693, N1-0095 and the bilateral grant BI-CN-18-20-008).

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