Reliability Evaluation of Augmented Cubes on Degree.

The n -dimensional augmented cube A Q n , proposed by Choudum and Sunitha in 2002, is one of the most famous interconnection networks of the distributed parallel system. Reliability evaluation of underlying topological structures is vital for fault tolerance analysis of this system. As one of the most extensively studied parameters, the k -conditional edge-connectivity of a connected graph G , λ k (G) , is defined as the minimum number of the cardinality of the edge-cut of G , if exists, whose removal disconnects this graph and keeps each component of G − F having minimum degree at least k. Let n , t and δ be three integers, where δ = 1 , if t = 0 and δ = 0 , if t > 0. In this paper, we determine the exact value of the (2 t − 1) -conditional edge-connectivity of A Q n , λ 2 t − 1 (A Q n) = 2 t (2 n − 2 t) − δ for each positive integer 0 ≤ t ≤ n − 1 and n ≥ 1 , and give an affirmative answer to Shinde and Borse's corresponding conjecture on this topic in [On edge-fault tolerance in augmented cubes, J. Interconnection Netw. 20(4) (2020), DOI:10.1142/S0219265920500139 ]. [ABSTRACT FROM AUTHOR]