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THE GENERAL POSITION NUMBER OF THE CARTESIAN PRODUCT OF TWO TREES

Published online by Cambridge University Press:  04 December 2020

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]

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.

Type
Research Article
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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