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 lambda(g)(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 >= 3e(g)(BHn)/g+1 and 9 <= g <= 2n - 1, where e(g)(BHn) = max{|E(BHn[U])vertical bar vertical bar U subset of V (BHn),vertical bar U vertical bar = g + 1}.