Given a graph G, a set is Δ-convex if there is no vertex u∈V(G)∖S forming a triangle with two vertices of S. The Δ-convex hull of S is the minimum Δ-convex set containing S. This article is an attempt to discuss the Carath\'eodory number and exchange number on various graph families and standard graph products namely Cartesian, strong and, lexicographic products of graphs.
@article{arxiv.2501.15025,
title = {Carath$\'{e}$odory Number and Exchange Number in $\Delta$-convexity},
author = {Bijo S. Anand and Arun Anil and Manoj Changat and Prasanth G. Narasimha-Shenoi and Sabeer S. Ramla},
journal= {arXiv preprint arXiv:2501.15025},
year = {2025}
}