On the general position set of two classes of graphs

TL;DR

This paper investigates the general position number in specific classes of graphs, providing bounds for cacti with cycles and pendant edges, and explicitly determining it for wheel graphs.

Contribution

It establishes bounds for the general position number in cacti graphs with cycles and pendant edges, and calculates it exactly for wheel graphs, advancing understanding of graph geometric properties.

Findings

Bounds for gp-number in cacti with k cycles and t pendant edges

Exact gp-number for wheel graphs

Enhanced understanding of vertex subsets avoiding geodesics

Abstract

The general position problem is to find the cardinality of a largest vertex subset S such that no triple of vertices of S lie on a common geodesic. For a connected graph G, the cardinality of S is denoted by gp(G) and called gp-number (or general position number) of G. In the paper, we obtain an upper bound and a lower bound regarding gp-number in all cactus with k cycles and t pendant edges. Furthermore, the gp-number of wheel graph is determined.