On the reliability and fault tolerance of spined cubes

Given a graph G and a non-negative integer g, the g-extra edge connectivity of G is the minimum cardinality of a set of edges in G, if it exists, whose deletion connects G and each remaining component will have more than g vertices. The spined cube, introduced by Zhou, et al. [The spined cube: A new hypercube variant with smaller diameter, Information Processing Letters, 111 (2011) 561-567.], is a new hypercube variant with smaller diameter. In this paper, we show that the 1-extra edge connectivity of the ridimensionai spined cube is 2n - 2 for n ≥ 3.