The generalized 4-connectivity of burnt pancake graphs

• Published in: Discrete Applied Mathematics Vol. 360; pp. 93 - 114
• Main Authors: Wang, Jing, Wu, Jiang, Ouyang, Zhangdong, Huang, Yuanqiu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.01.2025
• Subjects: Burnt pancake graph; Generalized [formula omitted]-connectivity; Interconnection network; Tree; Interconnection network; Tree; Burnt pancake graph; Generalized k-connectivity
• ISSN: 0166-218X
• DOI: 10.1016/j.dam.2024.08.019

The generalized k-connectivity of a graph G, denoted by κk(G), is the minimum number of internally disjoint S-trees for any S⊆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 possesses many desirable properties. In this paper, we try to evaluate the reliability of BPn by investigating its generalized 4-connectivity. By introducing the definition of inclusive tree and by studying structural properties of BPn, we show that κ4(BPn)=n−1 for n≥2, that is, for any four vertices in BPn, there exist (n−1) internally disjoint trees connecting them in BPn.