The generalized 4-connectivity of pancake graphs

The generalized connectivity is a generalization of traditional connectivity, which is a parameter that can measure the capability of connecting vertices in G. The pancake graph has some desirable properties to design interconnection networks. In this paper, we obtain that the generalized 4-connectivity of pancake graph Pn is n -2, that is, there are (n - 2) internally disjoint S-trees connecting any four arbitrary vertices x, y, z and w of Pn, where S = {x, y, z, w}. As a corollary, the generalized 3-connectivity of the pancake graph Pn can be obtained directly. (c) 2022 Elsevier B.V. All rights reserved.