The generalized 4-connectivity of burnt pancake graphs

The generalized k-connectivity of a graph G, denoted by kappa(k)(G), is the minimum number of internally edge disjoint S-trees for any S subset of V(G) and |S|=k. The generalized k-connectivity is a natural extension of the classical connectivity and plays a key role in applications related to the modern interconnection networks. An n-dimensional burnt pancake graph BPn is a Cayley graph which posses many desirable properties. In this paper, we try to evaluate the reliability of BPn by investigating its generalized 4-connectivity. By introducing the notation of inclusive tree and by studying structural properties of BPn, we show that kappa(4)(BPn)=n-1 for n >= 2, that is, for any four vertices in BPn, there exist (n-1) internally edge disjoint trees connecting them in BPn. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.