Cluster connectivity and super cluster connectivity of half hypercube networks

Connectivity stands as a pivotal metric for evaluating the fault tolerance of interconnection networks. It measures the network's ability to maintain communication and operational continuity even in the face of failures. However, the traditional connectivity can not effectively reflect the fault tolerance ability of the network when failures occur in a clustered or block-like manner in the actual environment. To address this limitation, cluster connectivity and super cluster connectivity were proposed. In this paper, we explore the H (H⁎)-cluster connectivity and super H (H⁎)-cluster connectivity of the half hypercube network which is a hypercube-based compound network, where H∈{K1,r|0≤r≤⌈n/2⌉−4}.