Research Article

On the general position number of the k-th power graphs

Published in: Quaestiones Mathematicae
Volume 47 , issue 11 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 2215–2230
DOI: 10.2989/16073606.2024.2352568
Author(s): Jing Tian Zhejiang University of Science and Technology, China, Kexiang Xu Nanjing University of Aeronautics & Astronautics, China,
Keywords: 05C12, 05C05, 05C76, General position set, general position number, power graphs,
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Abstract

A set is called a general position set of a graph G if any triple set V 0 of R is non-geodesic, that is, three elements of V 0 cannot lie on the same geodesic of G. The general position number gp(G) of a graph G is the cardinality of a largest general position set of G. The k-th power, Gk , of a graph G is obtained from G by adding a new edge between each pair of vertices with a distance of at most k in G. In this paper we establish the bounds for gp(Gk ) and and give an explicit formula of . Also we consider the relation between gp(G 2) and gp(G). We deduce a formula of and provide the upper bound on gp(G 2)−gp(G) for general block graphs G. Moreover, we determine the gp-number for the square of trees.
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