Introduced and investigate the stability number for general position number of graphs

Let 𝐺 be a graph. A subset 𝑆⊆𝑉(𝐺) is said to be a general position of G if no geodesic (shortest path) of G contains more than two vertices of S. The maximum size of a general position set in G is called the general position number of 𝐺. In this work, we introduce the general position stability number, denoted by 𝑉 𝑆 𝑔𝑝 (G), as the minimum number of vertices whose deletion alters the general position number of 𝐺, while the graph remains connected. We determine this parameter for several well-known classes of graphs

Keywords:

graph , general position set , general position stability number