The $g$-extra edge-connectivity of balanced hypercubes

Abstract

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 BH n and conjectured that the g-extra edge-connectivity of BH n is λ g (BH n ) = 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 (BH n ) g + 1 and 9 ≤ g ≤ 2n − 1, where