The general position number of the Cartesian product of two trees

TL;DR

This paper proves that the general position number, which measures the largest set of vertices avoiding collinear triples on shortest paths, is additive when considering the Cartesian product of two trees.

Contribution

It establishes the additivity of the general position number specifically for the Cartesian product of two trees, a previously unresolved property.

Findings

The general position number is additive for the Cartesian product of two trees.

Provides a new understanding of the structure of general position sets in product graphs.

Advances theoretical knowledge in graph theory related to shortest paths and vertex configurations.

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.