Reliability of Half Hypercube Networks under Cluster Faults

Malicious attackers frequently aim to partition the network into disjointed segments to facilitate specific attacks. Consequently, enhancing network reliability stands as an effective preventive measure. Connectivity serves as a crucial metric for gauging network reliability, yet classical connectivity inadequately captures a network's fault tolerance in the face of such attacks. To address this, cluster connectivity has been proposed, considering the faults within clusters to improve fault tolerance assessment. In this paper, we establish the cluster connectivity of the half hypercube network HH
n
. In detail, we show that the K
1,1
-cluster connectivity of HH
n
is $\left\lfloor {n/2} \right\rfloor + 1$, where n ≥ 3, and the K
1,r
- cluster connectivity of HH
n
is $\left\lceil {\frac{{\left\lceil {n/2} \right\rceil }}{2}} \right\rceil + 1$, where n ≥ 5 and 2 ≤ r ≤ 4, which is almost r times the classical connectivity. This indicates that the network possesses an enhanced capacity to accommodate a greater number of faulty nodes, potentially enabling more effective orchestration of attacks.