The h-Extra r-Component Connectivity of Half Hypercube

To support the design of more reliable parallel and distributed systems, this work delves into the fault tolerance of interconnection networks and investigates the Formula: see text-extra Formula: see text-component connectivity of networks. The Formula: see text-extra Formula: see text-component connectivity of a connected network Formula: see text, denoted by Formula: see text, is defined as the minimum cardinality of a vertex set whose removal disconnects Formula: see text into at least Formula: see text components, each having at least Formula: see text vertices. This paper focuses on the Formula: see text-extra Formula: see text-component connectivity of Formula: see text-dimensional half hypercube networks Formula: see text and derives formulas for Formula: see text-extra Formula: see text-component connectivity and Formula: see text-extra Formula: see text-component connectivity of Formula: see text: Formula: see text (Formula: see text) and Formula: see text (Formula: see text). Furthermore, we prove that the upper bound Formula: see text (Formula: see text) is tight for Formula: see text and Formula: see text, providing more accurate and valuable insights into the Formula: see text-extra Formula: see text-component connectivity of Formula: see text.