The k -Regular Edge Connectivity of Three Types of Regular Graphs
Li Wang, LR Lin, Yanxia Zhao · International Journal of Foundations of Computer Science · 2025
Let G be a connected graph. The k-regular edge cut F of G is a subset of [Formula: see text] such that [Formula: see text] is disconnected and each component is k-regular. The k-regular edge connectivity of G, denoted as [Formula: see text], is the minimum cardinality of a k-regular edge cut in G. It is a generalization of traditional connectivity, which has better fault tolerability. In this paper, we determine the k-regular edge connectivity of three categories of graphs, which are pancake graph [Formula: see text], burnt pancake graph [Formula: see text] and godan graph [Formula: see text]. Moreover, [Formula: see text] for [Formula: see text] ([Formula: see text]), [Formula: see text] for [Formula: see text] ([Formula: see text]) and [Formula: see text] for [Formula: see text] ([Formula: see text]) are shown.