The 3-path-connectivity of burnt pancake graph

Given a connected graph G. For a set Ω⊆V(G) with size at least two, an Ω-path refers to a path that includes every vertex in Ω, and two Ω-paths are internally disjoint if they are edge disjoint and share no vertices outside of Ω. The k-path-connectivity, denoted by πk(G), refers to the minimal number of mutually internally disjoint Ω-paths that exist in G, where the minimum is computed across all subsets Ω⊆V(G) of size k. This parameter generalizes the classical vertex connectivity. This paper focuses on determining the 3-path-connectivity of the n-dimensional burnt pancake graph BPn. By exploring its properties and analyzing the construction of internally disjoint paths, we prove that π3(BPn)=⌊3n−14⌋ for n≥2.