The g-Extra Edge-Connectivity of Balanced Hypercubes

The g-extra edge-connectivity is an important measure for the reliability of interconnection networks. Recently, Yang et al. [Appl. Math. Comput. 320 (2018) 464–473] determined the 3-extra edge-connectivity of balanced hypercubes BHn and conjectured that the g-extra edge-connectivity of BHn is λg(BHn) = 2(g + 1)n − 4g + 4 for 2 ≤ g ≤ 2n − 1. In this paper, we confirm their conjecture for n ≥ 6 − 12 g+1 and 2 ≤ g ≤ 8, and disprove their conjecture for n ≥ 3eg(BHn) g+1 and 9 ≤ g ≤ 2n − 1, where eg(BHn) =max{|E(BHn[U])|| U ⊆ V (BHn),|U| = g + 1}.