General position number of hierarchical scale-free graphs

Faculty of Education, University of the Ryukyus, 903-0213, 1, Sembaru, Nakagami-Gun Nishihara-Cho, Okinawa, Japan

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 5 June 2024
Accepted: 22 February 2026

Abstract

In this paper, we consider one of graph invariants, called a general position number, of scale-free graphs, where the scale-free property is one of key properties of real-world networks. To understand the tendency of general position numbers of scale-free graphs, we primarily deal with deterministic artificial scale-free graphs, since such graphs are very manageable and artificial models of complex networks mimic many properties of real-world networks. We derive estimates for the general position number of three well-known hierarchical scale-free graphs generated by deterministic models: one model produces fractal graphs, while the other two generate non-fractal graphs.