General position problems in strong and lexicographic products of graphs

TL;DR

This paper investigates various general position sets in strong and lexicographic graph products, establishing bounds and exact values for their sizes, advancing understanding of graph product properties.

Contribution

It provides new bounds and exact values for outer, dual, and total general position numbers in strong and lexicographic graph products.

Findings

Sharp bounds for outer and dual general position numbers in strong products.

Exact values for outer and total general position numbers in both products.

Determination of the dual general position number in many cases.

Abstract

Outer, dual, and total general position sets are studied on strong and lexicographic products of graphs. Sharp lower and upper bounds are proved for the outer and the dual general position number of strong products and several exact values are obtained. For the lexicographic product, the outer general position number is determined in all the cases, and the dual general position number in many cases. The total general position number is determined for both products. Along the way some results on outer general position sets are also derived.